Author: dweiss
Date: Tue Oct 13 10:21:45 2009
New Revision: 94
Added:
trunk/templates/example-msc-polish/
trunk/templates/example-msc-polish/.project
trunk/templates/example-msc-polish/01-wstep.tex
trunk/templates/example-msc-polish/02-podstawy.tex
trunk/templates/example-msc-polish/03-przeglad.tex
trunk/templates/example-msc-polish/04-algorytmy.tex
trunk/templates/example-msc-polish/05-testy.tex
trunk/templates/example-msc-polish/06-zakonczenie.tex
trunk/templates/example-msc-polish/a1-vm.tex
trunk/templates/example-msc-polish/a2-web-resources.tex
trunk/templates/example-msc-polish/bibliography.bib
trunk/templates/example-msc-polish/figures/
trunk/templates/example-msc-polish/figures/KS.pdf (contents, props changed)
trunk/templates/example-msc-polish/figures/blindtrie.pdf (contents, props
changed)
trunk/templates/example-msc-polish/figures/bucket-refinement.pdf (contents,
props changed)
trunk/templates/example-msc-polish/figures/gviz.sh (contents, props
changed)
trunk/templates/example-msc-polish/figures/mississippi.gviz
trunk/templates/example-msc-polish/figures/mississippi.pdf
trunk/templates/example-msc-polish/figures/mississippi_trie.gviz
trunk/templates/example-msc-polish/figures/mississippi_trie.pdf (contents,
props changed)
trunk/templates/example-msc-polish/figures/reduced-string-sorting.pdf
(contents, props changed)
trunk/templates/example-msc-polish/figures/results/
trunk/templates/example-msc-polish/figures/results/gauntlet-compare.pdf
trunk/templates/example-msc-polish/figures/results/harmony-gauntlet.pdf
trunk/templates/example-msc-polish/figures/results/harmony-manzini.pdf
trunk/templates/example-msc-polish/figures/results/ibm-gauntlet.pdf
trunk/templates/example-msc-polish/figures/results/ibm-manzini.pdf
trunk/templates/example-msc-polish/figures/results/jrockit-gauntlet.pdf
trunk/templates/example-msc-polish/figures/results/jrockit-manzini.pdf
trunk/templates/example-msc-polish/figures/results/manzini-compare.pdf
trunk/templates/example-msc-polish/figures/results/random-alphabet-lcp.pdf
trunk/templates/example-msc-polish/figures/results/random-alphabet-time.pdf
trunk/templates/example-msc-polish/figures/results/random-input-lcp-100.pdf
trunk/templates/example-msc-polish/figures/results/random-input-lcp-255.pdf
trunk/templates/example-msc-polish/figures/results/random-input-lcp-4.pdf
trunk/templates/example-msc-polish/figures/results/random-input-lcp.pdf
trunk/templates/example-msc-polish/figures/results/random-input-memory-100.pdf
trunk/templates/example-msc-polish/figures/results/random-input-memory-255.pdf
trunk/templates/example-msc-polish/figures/results/random-input-memory-4.pdf
trunk/templates/example-msc-polish/figures/results/random-input-time-100.pdf
trunk/templates/example-msc-polish/figures/results/random-input-time-255.pdf
trunk/templates/example-msc-polish/figures/results/random-input-time-4.pdf
trunk/templates/example-msc-polish/figures/results/sun-gauntlet.pdf
trunk/templates/example-msc-polish/figures/results/sun-manzini.pdf
trunk/templates/example-msc-polish/figures/template/
trunk/templates/example-msc-polish/figures/template/logo-pp.eps
trunk/templates/example-msc-polish/figures/template/logo-pp.pdf (contents,
props changed)
trunk/templates/example-msc-polish/figures/zorroST.gviz
trunk/templates/example-msc-polish/figures/zorroST.pdf (contents, props
changed)
trunk/templates/example-msc-polish/figures/zorroSTrie.gviz
trunk/templates/example-msc-polish/figures/zorroSTrie.pdf (contents, props
changed)
trunk/templates/example-msc-polish/graphs/
trunk/templates/example-msc-polish/graphs/o.ps
trunk/templates/example-msc-polish/graphs/readme.txt
trunk/templates/example-msc-polish/graphs/sample.dot
trunk/templates/example-msc-polish/mnowak-master-thesis.pdf
trunk/templates/example-msc-polish/mnowak-master-thesis.tex
trunk/templates/example-msc-polish/ppfcmthesis.cls
trunk/templates/example-msc-polish/tables/
trunk/templates/example-msc-polish/tables/gauntlet.vm.compare.tex
trunk/templates/example-msc-polish/tables/harmony/
trunk/templates/example-msc-polish/tables/harmony/gauntlet.tex
trunk/templates/example-msc-polish/tables/harmony/manzini.tex
trunk/templates/example-msc-polish/tables/ibm/
trunk/templates/example-msc-polish/tables/ibm/gauntlet.tex
trunk/templates/example-msc-polish/tables/ibm/manzini.tex
trunk/templates/example-msc-polish/tables/jrockit/
trunk/templates/example-msc-polish/tables/jrockit/gauntlet.tex
trunk/templates/example-msc-polish/tables/jrockit/manzini.tex
trunk/templates/example-msc-polish/tables/manzini.vm.compare.tex
trunk/templates/example-msc-polish/tables/sun/
trunk/templates/example-msc-polish/tables/sun/gauntlet.tex
trunk/templates/example-msc-polish/tables/sun/manzini.tex
Removed:
trunk/templates/example-istencel/
trunk/templates/example-mbegier/
trunk/templates/example-thinkubator/
Log:
Updated the examples, removed old ones.
Added: trunk/templates/example-msc-polish/.project
==============================================================================
--- (empty file)
+++ trunk/templates/example-msc-polish/.project Tue Oct 13 10:21:45 2009
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<projectDescription>
+ <name>thesis-text</name>
+ <comment></comment>
+ <projects>
+ </projects>
+ <buildSpec>
+ <buildCommand>
+ <name>org.eclipse.ui.externaltools.ExternalToolBuilder</name>
+ <triggers>full,incremental,</triggers>
+ <arguments>
+ <dictionary>
+ <key>LaunchConfigHandle</key>
+
<value><project>/.externalToolBuilders/net.sourceforge.texlipse.builder.Te\
xlipseBuilder.launch</value>
+ </dictionary>
+ </arguments>
+ </buildCommand>
+ </buildSpec>
+ <natures>
+ <nature>net.sourceforge.texlipse.builder.TexlipseNature</nature>
+ </natures>
+</projectDescription>
Added: trunk/templates/example-msc-polish/01-wstep.tex
==============================================================================
--- (empty file)
+++ trunk/templates/example-msc-polish/01-wstep.tex Tue Oct 13 10:21:45 2009
@@ -0,0 +1,65 @@
+\chapter{Wprowadzenie}
+
+% [DW] Cytowania normalnie, bez dodatkowych nawiasów; poprawiłem niektóre,
zrób pozostałe.
+
+Drzewa sufiksów oraz tablice sufiksów, czyli tablice leksykograficznie
posortowanych sufiksów pewnego
+ciągu symboli, znajdują wiele praktycznych zastosowań:
+
+\begin{itemize}
+ \item w~problemach przetwarzania tekstu, nazywanych
żargonowo~\emph{stringology}, takich
+ jak dopasowywanie, przeszukiwanie, wyszukiwanie powtarzających się
podciągów
+ i~maksymalnych sekwencji~\cite{Manber90, gusfield} oraz
+ wielu innych;
+
+ \item w~bioinformatyce~\cite{abouelhoda-genome}, gdzie
+ pytania dotyczące kodu genetycznego można sprowadzić do rozwiązania
problemów operujących
+ na ciągach znaków;
+
+ \item w~kompresji danych~\cite{BW}, gdzie wykorzystywane są do
wyszukiwania powtarzających
+ się sekwencji symboli i do obliczania transformacji Burrowsa-Wheelera
+ (\english{Burrows-Wheeler transform}, \akronim{BWT}), która jest krokiem
wstępnym
+ takich metod kompresji danych, jak np.~\texttt{bzip2}.
+\end{itemize}
+
+Większość z~powyższych problemów daje się efektywnie rozwiązać przy
pomocy
+drzew sufiksów (\english{suffix tree}). Udowodniono
jednakże~\cite{replacing},
+że tablice sufiksów są w~wielu przypadkach równie dobrą strukturą danych
co drzewa sufiksów,
+a~ponieważ ich konstrukcja jest zwykle obarczona
+mniejszym kosztem pamięciowym i~czasowym (mimo tej samej teoretycznej
+złożoności $\bigO(n)$), to właśnie tablice sufiksów cieszą się coraz
większym
+powodzeniem w~praktyce.
+
+Istnieje wiele algorytmów tworzenia tablic sufiksów, w~większości
opublikowanych wraz z~implementacjami
+w~języku \texttt{C} lub \texttt{C++}. O~ile od strony teoretycznej
+większość z~tych algorytmów jest efektywna (liniowa), o~tyle w~praktyce ich
efektywność zależy od aspektów
+dostępu do pamięci oraz wielkości słownika symboli. Brakuje również
+implementacji tych algorytmów w~językach wysokiego poziomu, takich jak język
Java.
+Tym brakiem właśnie motywujemy potrzebę opracowania w~języku Java
biblioteki algorytmów tworzenia
+tablic sufiksów. Przeniesienie samych algorytmów do języka Java wymaga
zwrócenia szczególnej uwagi na
+jego cechy specyficzne w~stosunku do języków niskiego poziomu -- różnice
w~dostępie do pamięci
+(brak wskaźników, relokowalne struktury danych), zarządzanie pamięcią
przez maszynę
+wirtualną (\emph{garbage collector}), czy też fakt, że kod programu
poddawany jest bezustannej obserwacji
+i~kompilacji w~czasie rzeczywistym (\emph{just in time compilation}).
+
+
+\section{Cel i~zakres pracy}
+
+Głównym celem tej pracy jest \textbf{wybór najlepszych algorytmów tworzenia
tablic sufiksów oraz
+ich efektywna implementacja w~postaci biblioteki napisanej w~języku Java}.
W~zakres pracy wliczony jest również przegląd obecnie dostępnej literatury
poświęconej metodom
+tworzenia tablic sufiksów oraz opis najciekawszych spośród nich. Docelowo
powinna powstać
+więc pewna taksonomia opierająca się na schemacie działania algorytmów
i~umożliwiająca ich porównanie i~odniesienie względem siebie.
+
+Drugim celem pracy jest dokładne przetestowanie i~analiza utworzonej
implementacji i~określenie jej wydajności na różnych
+maszynach wirtualnych oraz na różnych platformach sprzętowych. Uzyskane
wyniki eksperymentalne
+skonfrontowane zostaną z~istniejącymi wynikami testów wydajnościowych
implementacji tych
+samych algorytmów w~językach \texttt{C} i~\texttt{C++}.
+
+\section{Struktura pracy}
+
+W~rozdziałach drugim i~trzecim przedstawiono przegląd literatury
dziedzinowej; rozdział drugi
+zawiera podstawy teoretyczne wprowadzające czytelnika w~tematykę tablic
sufiksów, a~trzeci
+poświęcony jest klasyfikacji i~przeglądowi metod tworzenia tablic sufiksów.
Rozdział czwarty zawiera
+opisy wybranych algorytmów. W rozdziale piątym podane są wyniki empirycznych
testów
+wydajnościowych wykonanych w różnych środowiskach i na różnych maszynach
wirtualnych.
+Rozdział szósty stanowi podsumowanie pracy.
+
Added: trunk/templates/example-msc-polish/02-podstawy.tex
==============================================================================
--- (empty file)
+++ trunk/templates/example-msc-polish/02-podstawy.tex Tue Oct 13 10:21:45 2009
@@ -0,0 +1,208 @@
+\chapter{Podstawy teoretyczne}
+
+
+\section{Podstawowe pojęcia}
+
+Niech $\Sigma$ oznacza skończony zbiór o~rozmiarze $|\Sigma| \geq 1$, zwany
+dalej alfabetem \cite{taxonomy}. Elementami tego zbioru są symbole (w
przypadku tekstu
+zwykle utożsamiane z~pojedynczymi literami lub znakami). Alfabet określa się
+jako indeksowalny, jeżeli istnieje permutacja indeksów taka, że
+$\forall_{i=0..|\Sigma|-1}: a_0 < a_1 < \dots < a_{|\Sigma|-1}$
+(symbole mogą być uporządkowane).
+
+Niech $x$ oznacza ciąg symboli (pojęcia symbol, znak i~litera będą
+stosowane zamiennie) o~długości $n$.
+Element ciągu $x$ występujący na pozycji $i$ oznacza się jako $x[i]$, $i
\in
+\langle0, n-1\rangle$.
+Przez $x[a..b]$, $0 \leq a \leq b \leq n-1$ rozumie się
+podciąg $x$ rozpoczynający się na pozycji $a$, a~kończący na pozycji $b$
\cite{gusfield}.
+Warto zauważyć, że $x = x[0..n-1]$.
+
+\definicja{Prefiks} to taki podciąg $x$, którego pierwszy element
+jest jednocześnie pierwszym elementem ciągu $x$, tj.~$x[0..b]$, $0 \leq b
\leq
+n-1$.
+\definicja{Sufiks} oznacza taki podciąg $x$, którego ostatni element jest
+ostatnim znakiem ciągu $x$, tj. $x[a..n-1], 0 \leq a \leq n-1$. Przez
+$S^{x}_{i}$ (lub $S_i$ w~przypadku braku niejednoznaczności) rozumie się
+sufiks $x[i..n-1]$. Ciąg $x$ jest jednocześnie swoim najdłuższym prefiksem
jak i~sufiksem \cite{gusfield}.
+
+\definicja{Konkatenacją} dwóch ciągów $x$ i~$y$ o długości $n$ i~$m$
nazwiemy
+ciąg $z$, dla którego $z = x \circ y = x[0] x[1] .. x[n-1] y[0] y[1] ..
y[m-1]$.
+
+
+\section{Struktury danych}
+
+\definicja{Drzewo trie} (\english{trie}) \cite{larsson99structures} jest typem
+drzewa przeszukiwań, w~którym węzłom nie odpowiadają klucze, lecz ich
fragmenty. W~dalszej
+części pracy rozpatrywane będą drzewa, których kluczami są ciągi
+symboli z~pewnego alfabetu.\footnote{W nomenklaturze polskiej zarówno
+\emph{tree}, jak i~\emph{trie} nazywane są drzewami~\cite{pknuthv3}, str.~528.
+O~ile nie będzie powiedziane inaczej, przez drzewo będziemy
+rozumieli drzewo \emph{trie}.} W~tego typu drzewach
+krawędzie etykietowane są symbolami tego alfabetu, a~,,wartość'' klucza
danego węzła wynika z~jego
+pozycji i~jest konkatenacją etykiet krawędzi leżących na ścieżce
prowadzącej
+od korzenia drzewa do tego węzła. Wszystkie podwęzły danego
+węzła mają wspólny prefiks równy wartości klucza ich rodzica.
+Nieco inny wariant takiego drzewa, nazwany \definicja{drzewem skompresowanym}
+(\english{radix tree, Patricia trie}) \cite{larsson99structures}, polega na
tym, że węzły
+posiadające tylko jednego potomka są z~nimi łączone, a~symbole
z~usuniętych
+krawędzi są konkatenowane (zob.~rys.~\ref{rys:tree}).
+
+\begin{figure}[t]
+ \begin{center}
+ \includegraphics[scale=0.5]{figures/zorroSTrie.pdf}
+ \end{center}
+
+ \caption{Drzewo \emph{trie} dla zbioru sufiksów wyrazu ,,zorro'' z~dodanym
unikalnym
+ symbolem końcowym $\dollar$. Dla
+ przejrzystości pominięto łuk od korzenia do liścia o~wartości
$\dollar$.}%
+ \label{rys:tree}
+\end{figure}
+
+\definicja{Drzewo sufiksów} (\english{suffix tree}) \cite{gusfield} dla ciągu
symboli
+$x$ z~alfabetu $\Sigma$ jest skompresowanym drzewem zbudowanym na zbiorze
wszystkich sufiksów
+$x$ o~następujących cechach:
+\begin{itemize}
+ \item krawędzie są etykietowane niepustymi ciągami symboli,
+ \item każdy sufiks jest reprezentowany w~drzewie jako ścieżka od korzenia
+ do liścia,
+ \item wszystkie węzły wewnętrzne drzewa posiadają co najmniej dwóch
+ potomków.
+\end{itemize}
+
+Zwyczajowo na końcu ciągu $x$ umieszczany jest znak specjalny $\dollar$,
+leksykograficznie mniejszy od wszystkich symboli z~alfabetu $\Sigma$. Dzięki
temu zabiegowi
+żaden sufiks ciągu $x$ nie będzie prefiksem innego sufiksu, co zapewnia
zachowanie wszystkich wyżej
+wymienionych własności (w przeciwnym przypadku sufiksy mogłyby kończyć
się
+w~węzłach wewnętrznych drzewa). Rysunek \ref{rys:suffix-tree} prezentuje
+drzewo sufiksów dla sekwencji ,,zorro\$''. Trzy ,,klasyczne'' algorytmy
+tworzenia drzew sufiksów omówione zostały w~publikacjach \cite{weiner},
\cite{mccreight}
+i~\cite{ukkonen}. Ich porównanie można znaleźć w~pracy \cite{from-ukkonen}.
+
+\begin{figure}[t]
+ \begin{center}
+ \includegraphics[scale=0.5]{figures/zorroST.pdf}
+ \end{center}
+ \caption{Drzewo sufiksów wyrazu ,,zorro\$''. Dla przejrzystości
pominięto łuk od korzenia do
+ liścia o~wartości $\dollar$.}%
+ \label{rys:suffix-tree}
+\end{figure}
+
+W~literaturze powszechne jest etykietowanie sufiksów pozycją
+ich pierwszego symbolu w~słowie $x$ -- przez sufiks o~etykiecie i~rozumie
+się podciąg $x[i..n-1]$. \definicja{Tablica sufiksów} (\english{suffix
+array}) \cite{taxonomy} słowa $x$~jest tablicą etykiet sufiksów
uporządkowaną rosnąco według porządku
+leksykograficznego sufiksów.
+Tablicę sufiksów słowa $x$ oznacza się $\textit{SA}_x$ lub $\textit{SA}$
jeżeli pominięcie
+identyfikatora słowa nie wprowadza niejednoznaczności. Formalnie,
+$\textit{SA}[j] = i \iff x[i..n-1]$ jest $j$-tym sufiksem
+słowa $x$ według porządku leksykograficznego. Warto zauważyć, że
+$\textit{SA}$ jest zawsze permutacją liczb $0..n-1$. Rysunki
+\ref{rys:suffix-array-vis} oraz \ref{rys:suffix-array}
+prezentują tablicę sufiksów sekwencji symboli ,,zorro\$''.
+
+\begin{figure}[t]
+ \begin{center}
+ \begin{tabular}{ c c l }
+ \toprule
+ $j$ & $\textit{SA}[j]=i$ & $x[i..n-1]$ \\
+ \midrule
+ 0 & 5 & $\dollar$ \\
+ 1 & 4 & o$\dollar$ \\
+ 2 & 1 & orro$\dollar$ \\
+ 3 & 3 & ro$\dollar$ \\
+ 4 & 2 & rro$\dollar$ \\
+ 5 & 0 & zorro$\dollar$ \\
+ \bottomrule
+ \end{tabular}
+ \end{center}
+\caption{Tablica sufiksów dla sufiksów ciągu ,,zorro\dollar''.}%
+\label{rys:suffix-array-vis}
+\end{figure}
+
+Dla tablicy sufiksów można zbudować \definicja{tablicę najdłuższych
wspólnych podciągów}
+(\english{longest common prefix array}) \cite{taxonomy} o~długości $n$,
której elementy
+$\textit{lcp}[i], i = 1..n-1$ oznaczają długość najdłuższego wspólnego
prefiksu sufiksów
+$\textit{SA}[i]$ i~$\mathit{SA}[i-1]$. Przykładowa tablica najdłuższych
wspólnych prefiksów
+zaprezentowana jest na rysunku \ref{rys:suffix-array}. Tablicę $\textit{lcp}$
można obliczyć
+w~czasie liniowym znając \SA{} zgodnie z~metodami omówionymi w~artykułach
\cite{lcp-kasai}
+i~\cite{lcp-manzini}.
+
+Strukturą komplementarną do tablicy sufiksów $\textit{SA}$ jest
\definicja{odwrotna tablica
+sufiksów} (\english{inverse suffix array}) \cite{taxonomy} oznaczana jako
$\textit{ISA}$. Jest ona
+permutacją liczb $0..n-1$ spełniającą zależność: $\textit{ISA}[i] = j
\iff \textit{SA}[j] = i$.
+Przykład odwrotnej tablicy sufiksów znajduje się na rysunku
\ref{rys:suffix-array}. Wartość $k$-tego
+wpisu w~tablicy \SA{} oznacza identyfikator sufiksu na $k$-tej pozycji
w~porządku leksykograficznym;
+$k$-ty wpis w~tablicy \ISA{} oznacza pozycję sufiksu $k$ w~tablicy \SA{} (oraz
w~porządku
+leksykograficznym).
+
+\begin{figure}[t]
+ \begin{center}
+ \begin{tabular}{ r c c c c c c l}
+ & 0 & 1 & 2 & 3 & 4 & 5 & \\ \cmidrule{2-7}
+ $x = [$ & z & o & r & r & o & $\dollar$ & ] \\
+ $\mathit{SA} = [$ & 5 & 4 & 1 & 3 & 2 & 0 & ] \\
+ $\mathit{ISA} = [$ & 5 & 2 & 4 & 3 & 1 & 0 & ] \\
+ $\mathit{lcp} = [$ & - & 0 & 1 & 0 & 1 & 0 & ] \\
+ \end{tabular}
+ \end{center}
+\caption{Tablica sufiksów $\mathit{SA}$, odwrotna tablica sufiksów
$\mathit{ISA}$
+oraz tablica najdłuższych prefiksów $\mathit{lcp}$ dla sekwencji
+,,zorro\dollar''.}%
+\label{rys:suffix-array}
+\end{figure}
+
+Przez \definicja{h-grupę} (\english{h-group}) \cite{taxonomy} rozumie się
podzbiór
+sufiksów słowa $x$ o~wspólnym prefiksie długości $h>0$.
+Podział sufiksów na \emph{h-grupy} otrzymuje się poprzez ich częściowe
+uporządkowanie ze względu na wartość $h$~pierwszych symboli sufiksu.
+Proces ten nosi nazwę \emph{h-sortowania} (\english{h-sort}), w~jego
+wyniku sufiksy uporządkowane są według \emph{h-porządku}
+(\english{h-order}). Sufiksy należące do jednej \emph{h-grupy} są sobie
+równe pod względem \emph{h-porządku}. Algorytmy \emph{h-sortowania}
+są zazwyczaj stabilne, czyli zachowują wcześniejszy porządek sufiksów.
+Każdej \emph{h-grupie} można przypisać pewien identyfikator
+(\english{h-rank}). W~zależności od potrzeb algorytmu, wartości
+identyfikatorów dobierane są na jeden z~trzech sposobów:
+\begin{enumerate}
+ \item grupa identyfikowana jest pozycją pierwszego jej elementu
w~przybliżonej tablicy sufiksów -- głowa (\english{head}) grupy,
+ \item grupa identyfikowana jest pozycją ostatniego elementu w~przybliżonej
+ tablicy sufiksów -- ogon (\english{tail}) grupy,
+ \item każdej z~\emph{h-grup} (nawet jednoelementowym) przypisywane są
+ rosnące identyfikatory zgodnie z~kolejnością ich pojawienia się
w~$\textit{SA}_h$.
+\end{enumerate}
+
+\noindent
+Wyniki \emph{h-sortowania} zachowuje się w~\definicja{przybliżonej
+tablicy sufiksów} (\english{approximate suffix array}) \cite{taxonomy}
oznaczanej
+$\textit{SA}_h$. Możliwe jest również wyznaczenie
+\definicja{przybliżonej odwrotnej tablicy sufiksów}
+(\english{approximate inverse suffix array}) \cite{taxonomy} $\textit{ISA}_h$.
+$\textit{SA}_h$ jest permutacją liczb $0..n-1$, natomiast
+$\textit{ISA}_h$ może zawierać wartości powtarzające się. Wynika to
z~tego,
+że każdemu sufiksowi należącemu do danej \emph{h-grupy} przypisywany jest
jej identyfikator.
+Przykład przybliżonej tablicy sufiksów znajduje się na rysunku
\ref{rys:approx-suffix-array}.
+
+\begin{figure}[t]
+ \begin{center}
+ \begin{tabular}{ r c c c c c c c c c c c c l}
+ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9
& 10 & 11 \\ \cmidrule{2-13}
+ $x = [$ & a & b & e & a & c & a & d & a & b & e
& a &
+ $\dollar$ &]\\ $\mathit{SA}_1 = [$ & 11 & (0 & 3 & 5 &
7 & 10) & (1 & 8) & 4 & 6 & (3 & 9) & ] \\
+ $\mathit{ISA}_1 = [$ & 1 & 6 & 10 & 1 & 8 & 1 & 9 & 1 & 6 &
10 & 1 & 0 & ]\\
+ lub [ & 5 & 7 & 11 & 5 & 8 & 5 & 9 & 5 & 7 &
11 & 5 & 0 & ]\\
+ lub [ & 1 & 3 & 5 & 1 & 3 & 1 & 4 & 1 & 2 & 5
& 1 & 0 & ]\\
+ \end{tabular}
+ \end{center}
+\caption{Przykłady przybliżonej tablicy sufiksów oraz przybliżonej
+odwrotnej tablicy sufiksów dla $h=1$. \emph{H-grupy}
+wyróżnione zostały nawiasami. Na rysunku przedstawione są 3 wersje tablicy
+$\textit{ISA}_1$ różniące się metodami przypisywania identyfikatorów
grupom
+(wypisane w~kolejności przedstawienia w~tekście). Źródło:
\cite{taxonomy}.}%
+\label{rys:approx-suffix-array}
+\end{figure}
+
+W~niektórych publikacjach przyjęto inną konwencję nazewniczą,
\emph{h-grupa} nazywana
+jest tam \emph{h-kubełkiem} lub po prostu \emph{kubełkiem}
(\english{bucket}).
+Tablica $\textit{ISA}_h$ nazywana jest \definicja{tablicą wskaźników na
kubełki}
+(\english{bucket pointer array}) \cite{schurmann-phd}.
Added: trunk/templates/example-msc-polish/03-przeglad.tex
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+\chapter{Podział metod tworzenia tablic sufiksów}
+
+Tablice sufiksów zostały przedstawione w~roku 1990 przez Udiego Manbera
i~Gene'a
+Mayersa wraz z~pierwszym algorytmem ich tworzenia \cite{Manber90}.
+Zestawienie ważniejszych algorytmów tworzenia tablic sufiksów
+znajduje się w~tabeli \ref{tab:alg}. Autorzy pracy \cite{taxonomy}
podsumowują
+obecny stan wiedzy na temat tworzenia tablic sufiksów w~trzech punktach:
+\begin{itemize}
+ \item istnieją algorytmy efektywne pamięciowo o~złożoności liniowo
zależnej
+ od długości wejścia, np. \emph{smaller-larger}, \emph{skew},
+ \item istnieją algorytmy szybsze w~praktycznych zastosowaniach pomimo swojej
+ nieliniowej pesymistycznej złożoności, np. \emph{bpr}, \emph{improved
two-stage}, \emph{deep shallow}.
+ \item każdy problem, którego rozwiązanie można znaleźć z~pomocą drzew
sufiksów
+ może zostać rozwiązany w~tym samym czasie przy pomocy tablic sufiksów
+ \cite{replacing}.
+\end{itemize}
+
+\noindent
+Niezrealizowanym do tej pory celem jest zaprojektowanie takiego algorytmu
+tworzenia tablic sufiksów, który (za \cite{taxonomy}):
+\begin{itemize}
+ \item posiada minimalną złożoność asymptotyczną $\Theta(n)$,
+ \item jest szybki \emph{w~praktyce}, to znaczy na dużych rzeczywistych
+ zbiorach danych, np. [\ref{hart}],
+ \item jest \emph{lekki} -- wymaga niewiele więcej pamięci ponad ilość
+ potrzebną do przechowania $x$ i~\SA{x}.
+\end{itemize}
+
+
+\noindent
+Autorzy prac \cite{taxonomy} oraz \cite{schurmann-phd} podjęli próbę
stworzenia taksonomii
+metod tworzenia tablic sufiksów. Proponowane przez nich metody są do siebie
bardzo podobne,
+a~klasyfikacja proponowana przez \cite{taxonomy} została rozbudowana w~pracy
\cite{schurmann-phd}.
+
+W~dalszej części pracy omówiona zostanie klasyfikacja proponowana przez
Klausa-Bernda Schürmanna
+\cite{schurmann-phd} poszerzona o~algorytm \emph{improved two-stage}.
+
+\begin{table}[t]
+ \begin{center}
+ \begin{tabular}{l c c c }
+ \toprule
+ Algorytm & Publikacja &
Złożoność obliczeniowa & Złożoność pamięciowa \\ \midrule
+ \emph{bpr} & \cite{schurmann-phd} & $\bigO
(\frac{n^2}{\log n})$ & $9-10n$ \\
+ \emph{cache} & \cite{seward} &
$\bigO(n^2 \log n)$ & $9n$ \\
+ \emph{copy} & \cite{seward} &
$\bigO(n^2 \log n)$ & $5n$ \\
+ \emph{deep shallow} & \cite{MF} &
$\bigO(n^2 \log n)$ & $5n$ \\
+ \emph{difference-cover} & \cite{Burkhardt2003} & $\bigO(n
\log n)$ & $5-6n$ \\
+ \emph{improved two-stage} & \cite{MP} &
$\bigO(n^2 \log n)$ & $5n$ \\
+ \emph{odd-even} & \cite{kim} i~\cite{kim-jo-park} & $\bigO(n
\log \log n)$ & -- \\
+ \emph{prefix-doubling} & \cite{Manber90} &
$\bigO(n\log n)$ & $8n$ \\
+ \emph{qsufsort} & \cite{LS} &
$\bigO(n\log n)$ & $8n$ \\
+ \emph{skew} & \cite{KS} &
$\bigO(n)$ & $10-13n$ \\
+ \emph{smaller-larger} & \cite{Ko2005} &
$\bigO(n)$ & $7-10n$ \\
+ \emph{two-stage} & \cite{IT} &
$\bigO(n^2 \log n)$ & $5n$ \\
+ \bottomrule
+ \end{tabular}
+ \end{center}
+ \caption{Zestawienie ważniejszych metod tworzenia tablic sufiksów.
+ Złożoność pamięciowa podana jest dla sytuacji, gdy jeden symbol
zajmuje 1
+ jednostkę pamięci a~jedna liczba -- 4 jednostki pamięci. Źródło:
opracowanie
+ własne na podstawie \cite{taxonomy} i~\cite{schurmann-phd}.}%
+ \label{tab:alg}
+\end{table}
+
+
+\section{Podział metod ze względu na proces sortowania sufiksów}
+
+W~pracy \cite{schurmann-phd} zaproponowano dwa ortogonalne typy klasyfikacji
+algorytmów: pierwszy z~nich dzieli algorytmy ze względu na przebieg procesu
+sortowania sufiksów; drugi ze
+względu na sposób wykorzystania zależności między sufiksami. Podział
+algorytmów według obu typów klasyfikacji przedstawiony jest w~tabeli
+\ref{tab:schurmann}.
+
+Klasyfikacja algorytmów ze względu na proces sortowania sufiksów opiera się
na
+odpowiedzi na pytanie: ,,które sufiksy są przetwarzane w~pierwszej
kolejności
+i~jak przebiega dalej proces sortowania?''. Algorytmy dzielone są następnie
na
+dwie podgrupy: wykorzystujące \definicja{polepszanie kubełków}
(\english{bucket
+refinement}) oraz \definicja{sortowanie zredukowanych ciągów znaków}
(\english{reduced string sorting}).
+
+
+\subsection{Polepszanie kubełków}
+
+Pod pojęciem polepszania kubełków kryje się utworzenie \emph{k-porządku}
+sufiksów na podstawie wyliczonego wcześniej \emph{h-porządku} sufiksów
($k>h$).
+
+Pierwszy typ algorytmów wykorzystujących polepszanie kubełków opiera się
na ogólnych metodach
+sortowania ciągów znaków (które nie wykorzystują wiedzy o~zależnościach
między sufiksami). Algorytmy
+tego typu wykonują \emph{h-sortowanie} dla zwiększającego się $h$ dopóki
wszystkie \emph{h-grupy}
+(kubełki) nie będą zawierały tylko jednego elementu. Algorytmy należące
do tej kategorii to
+\emph{MSD radix sort} omówiony w~pracy \cite{radix} i~\emph{multikey
quicksort}
+opisany~w~\cite{bentley}.
+
+Drugi typ algorytmów polepszania kubełków opiera się na następującej
obserwacji: jeżeli dwa sufiksy
+słowa $x$ $x[u,n-1]$ i~$x[v,n-1]$ mają wspólny prefiks długości $\ell$, to
ich porządek można
+wywnioskować na podstawie porządku ich $\ell\textit{-następców}$ $x[u+\ell,
n-1]$ i~$x[v+\ell, n-1]$
+(przykładem tego procesu jest drugi etap algorytmu \emph{two-stage}).
Algorytmy z~tej grupy można
+podzielić na dwa dalsze podtypy:
+\begin{itemize}
+ \item algorytmy wykonujące \definicja{polepszanie wszerz}
+ (\english{breadth-first refinement}). Metody te dokonują \emph{h-sortowania}
+ ze zwiększającym się $h$~aż do uzyskania jednoelementowych kubełków
+ (\emph{h-grup}). Do tej grupy algorytmów należą \emph{prefix-doubling}
+ \cite{Manber90} i~\emph{qsufsort} \cite{LS}.
+
+ \item algorytmy wykonujące \definicja{polepszanie wgłąb}
(\english{depth-first
+ refinement}).
+ Metody te wykorzystują następujący schemat polepszania kubełków: dla
dowolnego
+ $h$, sortowanie sufiksów kolejnego kubełka następuje dopiero po tym, gdy
+ poprzedni kubełek jest w~pełni posortowany, czyli wszystkie jego podkubełki
są
+ jednoelementowe. Na przykład, dla ciągu ,,,AAABBABBBAAABBAB'' po
+ \emph{1-sortowaniu} grupa sufiksów rozpoczynających się od symbolu $B$
będzie
+ sortowana dopiero wtedy, gdy będzie ustalony porządek sufiksów
+ rozpoczynających się od $A$; podczas sortowania tej grupy porządek
sufiksów
+ o~prefiksie ,,AB'' będzie ustalony dopiero po posortowaniu sufiksów
rozpoczynających się od ,,AA'' itd.
+ Metody tego typu wykorzystują naiwne metody typu pierwszego w~sytuacji,
+ gdy porządek $\ell\textit{-następców}$ jest jeszcze nieznany.
+ Do tej kategorii algorytmów należą między innymi: \emph{two-stage},
\emph{copy},
+ \emph{cache} oraz \emph{deep shallow}. W~ogólności metody tego typu są
bardzo szybkie w~praktyce, pomimo ich wysokiej złożoności sięgającej nawet
$\bigO(n^2\log n)$.
+\end{itemize}
+
+Rysunek \ref{rys:bucket-refinement} przedstawia etapy procesu polepszania
+kubełków dla ciągu ,,AAABBABBBAAABBAB''. Każdy sufiks reprezentowany jest
przez
+pionową linię której wysokość oznacza jego pozycję według porządku
+leksykograficznego: niska linia oznacza sufiks leksykograficznie mniejszy od
+sufiksu reprezentowanego przez wyższą linię. Na rysunku
+\ref{rys:bucket-refinement} widać (od góry): stan początkowy, stan w~trakcie
+działania algorytmu (w przypadku polepszania wszerz jest to stan po
+posortowaniu według prefiksu długości 2; dla polepszania wgłąb jest to
stan po uporządkowaniu
+sufiksów rozpoczynających się od symbolu ,,A''), stan końcowy --
posortowane sufiksy.
+
+\begin{figure}[t]
+ \begin{center}
+ \includegraphics[scale=0.75]{figures/bucket-refinement.pdf}
+ \end{center}
+
+ \caption{Etapy algorytmu polepszania kubełków dla wyrazu
+ ,,AAABBABBBAAABBAB''. Źródło: \cite{schurmann-phd}.}%
+ \label{rys:bucket-refinement}
+\end{figure}
+
+
+\begin{table}[t]
+ \begin{center}
+ \begin{tabular}{l @{\hspace{2em}} c @{\hspace{2em}} c}
+ \toprule
+ Typ algorytmu & strategia \emph{push} &
strategia \emph{pull} \\
+ \midrule
+ Polepszanie wszerz & \emph{prefix-doubling} &
\emph{qsufsort} \\
+ \addlinespace[1em]
+ Polepszanie wgłąb & \emph{two-stage} &
\emph{cache} \\
+ & \emph{copy} &
\emph{bpr} \\
+ & \emph{deep-shallow} &
\\
+ & \emph{improved two-stage} &
\\
+ \addlinespace[1em]
+ Sortowanie zred.~ciągów znaków & \emph{skew} &
\emph{difference-cover} \\
+ & \emph{odd-even} &
\\
+ & \emph{smaller-larger} &
\\
+ \bottomrule
+ \end{tabular}
+ \end{center}
+ \caption{Podział algorytmów tworzenia tablic sufiksów według taksonomii
+ zaproponowanej w~pracy \cite{schurmann-phd}. Źródło: opracowanie własne
w~oparciu o~\cite{schurmann-phd}.}%
+ \label{tab:schurmann}
+\end{table}
+
+\subsection{Sortowanie zredukowanych ciągów znaków}
+
+Metody tego typu działają według następującego schematu: na początku
wybierany jest podzbiór
+\emph{sub} identyfikatorów sufiksów, odpowiadające im sufiksy są potem
sortowane na podstawie
+prefiksów ustalonej długości. Następnie każdemu z~tych sufiksów
przypisywany jest pewien klucz
+odpowiadający jego porządkowi wg. prefiksów. Następnie tworzony jest taki
ciąg $t^{\textit{sub}}$
+długości $|\textit{sub}|$ zawierający wcześniej przydzielone klucze,
którego \SA{t^{\textit{sub}}}
+odpowiada porządkowi leksykograficznemu sufiksów identyfikowanych zbiorem
\emph{sub}. Tablica
+\SA{t^{\textit{sub}}} może być obliczana rekurencyjnie tym samym algorytmem,
lub z~wykorzystaniem
+efektywnego algorytmu sortowania ciągów znaków (\cite{bentley-sort},
\cite{radix}, [\ref{ssort}],
+\cite{bentley}, \cite{sinha}). W~pełni uporządkowane sufiksy ze zbioru
\emph{sub} służą potem do
+posortowania pozostałych sufiksów. Ostatecznie budowana jest pełna tablica
sufiksów. Do algorytmów
+realizujących powyższy schemat należą: \emph{difference-cover},
\emph{skew}, \emph{odd-even} oraz
+\emph{smaller-larger}.
+
+Rysunek \ref{rys:reduced-string-sorting} przedstawia etapy działania algorytmu
+sortowania zredukowanych ciągów znaków. Podobnie jak na rysunku
+\ref{rys:bucket-refinement}, sufiksy reprezentowane są przez pionowe linie,
+których wysokość oznacza miejsce sufiksu w~porządku leksykograficznym.
Sufiks
+reprezentowany przez mniejszą linię jest leksykograficznie mniejszy od
sufiksu
+reprezentowanego przez wyższą linię. Na rysunku przedstawiono po kolei (od
+góry): stan początkowy; stan algorytmu w~sytuacji gdy posortowane są sufiksy
+o~nieparzystych identyfikatorach; stan końcowy.
+
+
+\begin{figure}[t]
+ \begin{center}
+ \includegraphics[scale=0.75]{figures/reduced-string-sorting.pdf}
+ \end{center}
+ \caption{Etapy algorytmu sortowania zredukowanych ciągów znaków dla
wyrazu
+ ,,AAABBABBBAAABBAB''. Źródło: \cite{schurmann-phd}.}%
+ \label{rys:reduced-string-sorting}
+\end{figure}
+
+\section{Podział ze względu na sposób wykorzystania zależności między
sufiksami}
+
+Drugim sposobem podziału zaproponowanym w~pracy \cite{schurmann-phd} jest
+podział algorytmów tworzenia tablic sufiksów ze względu na sposób
wykorzystania
+zależności między sufiksami. Jeżeli dwa sufiksy $x[u,n-1]$ i~$x[v,n-1]$
mają
+wspólny prefiks długości $\ell$, to ich porządek można ustalić na
podstawie
+porządku sufiksów $x[u+\ell,n-1]$ i~$x[v+\ell,n-1]$. Rozróżnia się dwie
metody
+wykorzystywania tej zależności: metodę \emph{pull} i~metodę
+\emph{push}.
+Terminy \emph{pull} i~\emph{push} pochodzą z~terminologii systemów
+informacyjnych, oznaczają różne strategie komunikacji pomiędzy nadawcą
+wiadomości i~jej odbiorcą. Metoda \emph{push} oznacza sytuację, kiedy
dostawca
+wiadomości nawiązuje komunikację. Odwrotna sytuacja następuje w~strategii
+\emph{pull} -- tutaj to odbiorca zgłasza żądanie inicjalizacji komunikacji.
+
+W~odniesieniu do algorytmów tworzenia tablic sufiksów metoda \emph{push}
polega na tym, że
+wykorzystuje porządek wcześniej obliczonych grup sufiksów do ustalenia
porządku grup sufiksów
+$\ell$\textit{-poprze\-dni\-ków}, tzn. po ustaleniu porządku sufiksów
$x[u+\ell,n-1]$ i~$x[v+\ell,n-1]$
+obliczany jest porządek sufiksów $x[u,n-1]$ i~$x[v,n-1]$. Wzorcowym
przykładem wykorzystania tej
+techniki jest algorytm \emph{two-stage}.
+
+Metoda \emph{pull} jest wykorzystywana w~procesie sortowania opierającego się
o~porównania. Podczas
+porównywania sufiksów $x[u,n-1]$ i~$x[v,n-1]$ sprawdzany jest porządek
sufiksów $x[u+\ell,n-1]$
+i~$x[v+\ell,n-1]$. Algorytm \emph{qsufsort} jest najlepszym przykładem
zastosowania tej techniki.
+
Added: trunk/templates/example-msc-polish/04-algorytmy.tex
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+
+\chapter{Wybrane metody tworzenia tablic sufiksów}
+
+W~poniższym rozdziale omówione są wybrane metody tworzenia tablic sufiksów.
+Algorytmy wybrane zostały na podstawie wyników testów wydajnościowych
+zaprezentowanych w~pracach \cite{taxonomy} i~\cite{schurmann-phd} oraz
+publikowanych na stronach [\ref{msufsort}] i~[\ref{mori-benchmark}].
+Algorytmy uzyskujące dobre wyniki na dużych zbiorach danych -- szybkie
\emph{w
+praktyce} pochodzą z~rodziny algorytmów wykorzystujących \emph{polepszanie
+wszerz}. W~poniższym zestawieniu opisane zostały również algorytmy
+reprezentujące inne grupy metod tworzenia tablic sufiksów: \emph{polepszanie
+wgłąb} i~\emph{sortowanie zredukowanych ciągów znaków}.
+
+
+\section{Algorytm \emph{skew}}
+
+Algorytm \emph{skew} został opracowany przez Petera Sandersa i~Juhę
+K\"arkk\"ainena \cite{KS}. Dostępna jest
+również implementacja tego algorytmu ich autorstwa [\ref{KScode}]. Opisywana
+metoda pochodzi z~rodziny algorytmów wykorzystujących
+\emph{sortowanie zredukowanych ciągów znaków}.
+Algorytm wykonuje 3 główne kroki:
+\begin{enumerate}
+ \item Tworzenie tablicy sufiksów zbudowanej z~sufiksów $S_i$ o~indeksach $i
+ \bmod{3} \neq 0$. Problem jest redukowany do tworzenia tablicy sufiksów
ciągu długości $2/3$
+ rozmiaru ciągu wejściowego, a~następnie rozwiązywany rekurencyjne.
+ \item Tworzenie tablicy sufiksów zbudowanej z~sufiksów pominiętych
w~pierwszym kroku z~wykorzystaniem tablic sufiksów z~kroku 1.
+ \item Połączenie zbudowanych tablic w~jedną.
+\end{enumerate}
+
+\noindent
+Pierwszy (i najbardziej czasochłonny) krok algorytmu polega na posortowaniu
+sufiksów $S_i$ dla $i \bmod{3} \neq 0$, czyli utworzeniu tablicy sufiksów
+$\textit{SA}^{12}$. Jeżeli w~wyniku \emph{h-sortowania} dla $h=3$ wszystkie
+grupy są jednoelementowe, to ten etap algorytmu się kończy. W~przeciwnym
przypadku
+każdemu sufiksowi $S_i$ nadawany jest identyfikator $x^{'}_i
+\in [ 1, 2n/3]$ będący identyfikatorem jego \emph{3-grupy} powstałej po
+\emph{3-sortowaniu}. Następnie tworzony jest ciąg $x^{12} = [x^{'}_i : i
+\bmod{3} = 1] \circ [x^{'}_i : i \bmod{3} = 2]$, którego tablica sufiksów
+$\textit{SA}_{x^{12}}$ obliczana jest rekurencyjnie. Tablica $\textit{SA}^{12}$
+wypełniana jest zgodnie z~poniższym wzorem ($n_1$ oznacza liczbę sufiksów
o~etykietach $i$ takich, że $i \bmod{3} = 1$):
+\begin{displaymath}
+\textit{SA}^{12}[i] = \left\{
+ \begin{array}{l l}
+ 1 + 3k & \textit{jeżeli } k = \textit{SA}_{x^{12}}[i] < n_1, \\
+ 2 + 3(k - n_1) & \textit{w przeciwnym wypadku}.
+ \end{array}
+ \right.
+\end{displaymath}
+
+Drugi krok algorytmu polega na utworzeniu tablicy sufiksów $\textit{SA}^0$
+złożonej z~sufiksów $S_i$, gdzie $i \bmod{3} = 0$. Tablica ta powstaje
w~wyniku
+sortowania par $(x[i], S_{i+1})$. Ponieważ porządek sufiksów $S_{i+1}$ jest
+zawarty w~$\textit{SA}^{12}$, do znalezienia $\textit{SA}^0$ wystarczy
posortować
+stabilnie elementy $\textit{SA}^{12}[j]$ reprezentujące sufiksy
+$\textit{SA}_{i+1}, i \bmod{3} = 0$ według wartości $x[i]$. Można tego
dokonać
+w~czasie liniowym jednym krokiem sortowania kubełkowego.
+
+Trzeci krok algorytmu polega na połączeniu tablic $\textit{SA}^{12}$
i~$\textit{SA}^0$ w~jedną
+tablicę sufiksów. Porównywanie sufiksów $S_j$, gdzie $j\bmod{3}=0$ i~$S_i,
i \bmod{3} \neq 0$
+odbywa się na jeden z~dwóch sposobów:
+\begin{itemize}
+ \item Jeżeli $i \bmod{3} = 1$, to porządek sufiksów $S_i$ i~$S_j$ można
+ ustalić porównując pary $(x[i], S_{i+1})$ oraz $(x[j], S_{j+1})$.
Ponieważ $i+1
+ \bmod{3} = 2$ i~$j+1 \bmod 3 = 1$ porządek sufiksów $S_{i+1}$ i~$S_{j+1}$
+ można ustalić na podstawie ich pozycji w~$\textit{SA}_{x^{12}}$. Ta pozycja
może
+ być ustalana w~czasie stałym, jeżeli obliczona zostanie tablica
+ $\textit{ISA}_{x^{12}}$.
+
+ \item Analogicznie, jeżeli $i \bmod{3} =
+ 2$, to porównywane są trójki $(x[i], x[i+1], S_{i+2})$ i~$(x[j], x[j+1],
S_{j+2})$, przy czym
+ sufiksy $S_{i+2}$ i~$S_{j+2}$ są zastępowane odpowiednimi wpisami z~tablicy
$\textit{ISA}_{x^{12}}$.
+\end{itemize}
+
+
+\begin{figure}[t]
+ \begin{center} \small
+ \begin{tabular}{r c c c c c c c c c c c c l}
+ & 0 & 1 & 2 & 3 & 4 & 5 & 6 &
7 & 8 & 9 & 10 & 11 \\ \cmidrule{2-13}
+ $x$ = [ & b & a & d & d & a & d & d &
a & c & c & a & $\dollar$ & ] \\
+$S_i, i \bmod{3} = 0$ = [ & 0 & & & 3 & & & 6 &
& & 9 & & & ] \\
+$S_i, i \bmod{3} \neq 0$ = [ & & 1 & 2 & & 4 & 5 & &
7 & 8 & & 10 & 11 & ] \\
+$x[i..i+2], i\bmod{3} \neq 0$ = [ & & add & dda & & add & dda & &
acc & cca & & a\$- & \$-- & ] \\ \addlinespace[1em]
+
+ \multicolumn{14}{c}{\emph{3-sortowanie} sufiksów o etykietach $i
\bmod{3} \neq 0$ (wartości są indeksami po posortowaniu).} \\
+ $x'$ = [ & & 3 & 5 & & 3 & 5 & &
2 & 4 & & 1 & 0 & ] \\ \addlinespace[1em]
+
+ \multicolumn{14}{c}{Tworzenie ciągu $x^{12} = [x^{'}_i : i
\bmod{3} = 1] \circ [x^{'}_i : i \bmod{3} = 2]$.} \\
+ $x^{12}$ = [ & 3 & 3 & 2 & 1 & 5 & 5 & 4 &
0 & ] \\ \addlinespace[1em]
+
+ \multicolumn{14}{c}{Obliczanie $\textit{SA}_{x^{12}}$ i
$\textit{SA}^{12}$.} \\
+ $\textit{SA}_{x^{12}}$ = [ & 7 & 3 & 2 & 1 & 0 & 6 & 5 &
4 & ] \\
+ $\textit{ISA}_{x^{12}}$ = [ & 4 & 3 & 2 & 1 & 7 & 6 & 5 &
0 & ] \\
+ $\textit{SA}^{12}$ = [ & 11 & 10 & 7 & 4 & 1 & 8 & 5 &
2 & ] \\ \addlinespace[1em]
+
+ \multicolumn{14}{c}{Sufiksy $S_i$, $i \bmod{3} = 1$ oraz $S_j$, $j
= i - 1$ zgodnie z kolejnością w $\textit{SA}^{12}$.} \\
+ ~ [ & 10 & 7 & 4 & 1 & ] \\
+ ~ [ & 9 & 6 & 3 & 0 & ] \\
+ $x[j]$ = [ & c & d & d & b & ] \\
\addlinespace[1em]
+
+ \multicolumn{14}{c}{Stabilne \emph{1-sortowanie} sufiksów $S_j$.}
\\
+ $\textit{SA}^0$ = [ & 0 & 9 & 6 & 3 & ] \\
\addlinespace[1em]
+
+ \multicolumn{14}{c}{Scalanie tablic $\textit{SA}^0$ i
$\textit{SA}^{12}$.} \\
+ $\textit{SA}$ = [ & 11 & 10 & 7 & 4 & 1 & 0 & 9 &
8 & 6 & 3 & 5 & 2 & ] \\
+ \end{tabular}
+ \end{center}
+ \caption{Przykład tworzenia tablicy sufiksów według algorytmu
\emph{skew}.
+ Źródło: opracowanie własne.}%
+ \label{rys:ks}
+\end{figure}
+
+
+\section{Algorytm \emph{qsufsort}}
+
+Algorytm \emph{qsufsort} został przedstawiony w~pracy \cite{LS} autorstwa
+Jespera Larrsona i~Kunihiko Sadakane. Autorzy pracę udostępniają również
+implementację w~języku \texttt{C} [\ref{LScode}]. Opisywana metoda należy do
+rodziny algorytmów wykonujących polepszanie wgłąb, opiera się na
algorytmie
+\emph{prefix-doubling}.
+
+Sortowanie sufiksów wykonywane jest algorytmem \emph{ternary split
+quicksort} \cite{bentley-sort}. Algorytm \emph{qsufsort} wykorzystuje
+również twierdzenie opublikowane w~pracy \cite{karp}: dla obliczonych \SA{h}
i~\ISA{h} posortowanie sufiksów $S_i$ według par (\ISA{h}$[i]$,
\ISA{h}$[i+h]$),
+$i+h \leq n$ tworzy \emph{2h-porządek} sufiksów, czyli
+porządek według prefiksów długości $2h$.\footnote{Sufiksy $S_i, i > n - h$
są
+zawsze w~pełni uporządkowane.}
+Wynika to z~tego, że do ustalenia porządku sufiksów o~wspólnym prefiksie
+długości $h$ wykorzystujemy porządek ich $\textit{h-następców}$, którzy
są
+również posortowani według h pierwszych znaków, co daje w~konsekwencji
porządek
+sufiksów według prefiksów długości $2h$.
+
+Na początku działania algorytm wykonuje \emph{1-sort}, w~wyniku którego
+powstają \SA{1} i~\ISA{1}. Numery grup w~odwróconej tablicy sufiksów
+przypisywane są poprzez wybór ogona (pozycji ostatniego sufiksu w~tablicy
+\SA{h}) danej grupy. Algorytm \emph{qsufsort} utrzymuje również tablicę $L$
+długości $n$ używaną w~celu określania rozmiarów grup.
+Wartość $L[j] = d$ oznacza, że grupa rozpoczynająca się na pozycji $j$ ma
$d$
+elementów. Wartości ujemne w~tablicy $L$ oznaczają ciągi jednoelementowych
+grup (na przykład $-2$ oznacza dwie jednoelementowe grupy).
+
+Przeglądanie tablicy $L$ od lewej do prawej umożliwia omijanie grup
+jednoelementowych w~procesie polepszania kubełków. Każda \emph{h-grupa}
+sortowana jest osobno, jej sufiksy $S_i$ porównywane są na podstawie
wartości
+\ISA{h}$[i+h]$. Po posortowaniu wszystkich grup otrzymujemy
\emph{2h-porządek}.
+Algorytm kończy swoje działanie, gdy wszystkie
+{h-grupy} są jednoelementowe, czyli gdy $L[0] = -n$. W~przeciwnym wypadku $h$
+jest podwajane, a~proces polepszania kubełków wykonywany po raz kolejny.
+
+ \begin{figure}[t]
+ \begin{center} \small
+ \begin{tabular}{ r c c c c c c c c c c c c l}
+ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11
\\\cmidrule{2-13}
+ $x$ = [ & a & b & e & a & c & a & d & a & b & e & a &
+ $\dollar$ & ] \\ \SA{1} = [ & 11 & (0 & 3 & 5 & 7 & 10) & (1 & 8) &
4 & 6 & (2 & 9) & ] \\
+ \ISA{1} = [ & 5 & 7 & 11 & 5 & 8 & 5 & 9 & 5 & 7 & 11 & 5 & 0
&] \\
+ $L$ = [ & -1 & 5 & & & & & 2 & & -2 & & 2 & &] \\
\cmidrule{2-13}
+ \SA{2} = [ & 11 & 10 & (0 & 7) & 3 & 5 & (1 & 8) & 4 & 6 & (2 & 9)
& ] \\
+ \ISA{2} = [ & 3 & 7 & 11 & 4 & 8 & 5 & 9 & 3 & 7 & 11 & 2 & 0
&] \\
+ $L$ = [ & -2 & & 2 & & -2 & & 2 & & -2 & & 2 & &] \\
\cmidrule{2-13}
+ \SA{4} = [ & 11 & 10 & (0 & 7) & 3 & 5 & 8 & 1 & 4 & 6 & 9 & 2
& ] \\
+ \ISA{4} = [ & 3 & 7 & 11 & 4 & 8 & 5 & 9 & 3 & 6 & 10 & 1 & 0
&] \\
+ $L$ = [ & -2 & & 2 & & -8 & & & & & & & &] \\
\cmidrule{2-13}
+ \SA{8} = [ & 11 & 10 & 7 & 0 & 3 & 5 & 8 & 1 & 4 & 6 & 9 & 2
& ] \\
+ \ISA{8} = [ & 3 & 7 & 11 & 4 & 8 & 5 & 9 & 2 & 6 & 10 & 1 & 0
&] \\
+ $L$ = [ & -12 & & & & & & & & & & & &] \\
+
+ \end{tabular}
+ \end{center}
+ \caption{Przebieg algorytmu \emph{qsufsort} dla słowa ,,abeacadabea''.
+ Źródło: opracowanie własne na podstawie \cite{taxonomy}.}%
+ \label{rys:ls}
+ \end{figure}
+
+Algorytm \emph{qsufsort} da się optymalizować pod kątem redukcji zużycia
+pamięci. Możliwe jest kompletne wyeliminowanie tablicy $L$. Do wyznaczania
\emph{h-grup} zawierających więcej niż 1 element można wykorzystać tablicę
+\ISA{}, rozmiar grupy wyznacza się wtedy na podstawie jej pierwszego elementu.
+Jeżeli $j$ oznacza pozycję pierwszego elementu grupy w~\SA{},
a~$i=$\SA{h}$[j]$, to jej rozmiar wynosi \ISA{h}$[i] - j + 1$.
+Złożoność pamięciowa algorytmu może również zostać zredukowana poprzez
+nadpisanie ciągu wejściowego i~wykorzystanie tego obszaru pamięci do
+przechowywania \ISA{} po obliczeniu \SA{1}.
+
+
+\section{Algorytm \emph{deep shallow}}
+
+Algorytm \emph{deep shallow} jest rozwinięciem algorytmu \emph{copy}
+opracowanym przez Paolo Ferraginę i~Giovanniego Manziniego. Opublikowany
został
+w~pracy \cite{MF}. Kod algorytmu w~języku \texttt{C} dostępny jest pod
adresem
+[\ref{MFcode}], jego autorem jest Giovanni Manzini.
+
+Pierwszym krokiem algorytmu jest uporządkowanie sufiksów według dwóch
+pierwszych znaków (\emph{2-sortowanie}). Każdy z~utworzonych w~ten
+sposób kubełków sortowany jest algorytmem \emph{multikey quicksort}
+\cite{bentley}, który jest przerywany po osiągnięciu poziomu rekurencji
równemu
+$L$, czyli jeżeli wewnątrz kubełka istnieje grupa sufiksów o~wspólnym
prefiksie
+długości $L$. Podejście to nosi nazwę sortowania płytkiego
(\english{shallow
+sorting}).
+
+Sortowanie znajdowanych sufiksów o~wspólnym prefiksie długości $L$
+nazwane zostało przez autorów algorytmu \emph{deep shallow} sortowaniem
+głębokim (\english{deep sort}). Przebieg działania głębokiego sortowania
zależy
+od wielkości zbioru sortowanych sufiksów. Jeżeli liczność zbioru nie
przekracza
+zadanej wartości $B$, to sufiksy są sortowane algorytmem \emph{blind sort}.
W~przeciwnym przypadku do posortowania sufiksów wykorzystane zostanie
zmodyfikowany algorytm
+\emph{ternary split quicksort} \cite{bentley-sort}. Autorzy sugerują użycie
+wartości $B = n \times 0.0005$ jako progu wielkości zbioru.
+
+Algorytm \emph{blind sort} opiera swoje działanie na strukturze danych
+nazywanej \definicja{blind trie} \cite{btree}, która jest typem
skompresowanego
+drzewa którego węzły wewnętrzne przechowują liczby określające
długość wspólnego
+prefiksu węzłów potomnych (jeżeli węzeł zawiera liczbę $k$, to jego
węzły
+potomne różnią się na pozycji $k+1$). Przykładowe drzewo \emph{blind trie}
+znajduje się na rysunku \ref{rys:blind-trie}.
+
+Algorytm \emph{blind sort} tworzy drzewo \emph{blind trie}, a~następnie
+przegląda je od lewej do prawej uzyskując w~ten sposób porządek
leksykograficzny
+sekwencji podanych na wejściu (w drzewie \emph{blind trie} węzły potomne
danego
+węzła są uporządkowane). Poważną wadą metody \emph{blind sort} jest jej
+złożoność pamięciowa, sięgająca nawet $36m$, gdzie $m$ oznacza liczbę
ciągów do
+posortowania.
+
+\begin{figure}[t]
+ \begin{center}
+ \includegraphics[width=.9\linewidth]{figures/blindtrie.pdf}
+ \end{center}
+ \caption{Drzewo skompresowane oraz odpowiadające mu drzewo \emph{blind
trie}
+ zbudowane na zbiorze sekwencji \emph{abaaba, abaabb, abac, bcbcaba,
bcbcabb, bcbcbba, bcbcbbba}.
+ Źródło: \cite{MF}.}\label{rys:blind-trie}
+\end{figure}
+
+Do sortowania zbiorów większych niż $B$ autorzy algorytmu \emph{deep
shallow}
+użyli zmodyfikowanego algorytmu \emph{ternary split quicksort}, opisanego
w~pracy \cite{bentley-sort}. Dokonali oni następujących zmian:
+\begin{enumerate}
+ \item Jeżeli na dowolnym etapie rekursji zbiór sufiksów jest mniejszy niż
+ $B$, to do jego sortowania użyty zostaje algorytm \emph{blind sort}.
+ \item Podczas fazy podziału sufiksów obliczane są $L_S$ i~$L_L$, czyli
+ długość najdłuższego wspólnego prefiksu elementu osiowego
(\english{pivot}) i~zbioru elementów mniejszych ($L_S$) oraz większych ($L_L$)
od elementu
+ osiowego. Dzięki temu podczas sortowania sufiksów w~tych zbiorach można
+ pomijać prefiksy długości $L_S$ lub $L_L$.
+\end{enumerate}
+
+Paolo Ferragina i~Giovanni Manzini w~pracy \cite{MF} wymieniają trzy zalety
+dwuetapowego podejścia do problemu sortowania sufiksów zastosowanego
w~algorytmie \emph{deep shallow}:
+\begin{enumerate}
+ \item Szybkie wykrywanie grup sufiksów o~długim wspólnym prefiksie.
+ \item Rozmiar stosu użytego podczas rekurencji w~fazie sortowania płytkiego
+ jest ograniczony parametrem $L$ i~nie zależy od rozmiaru wejścia.
+ \item Jeżeli długość najdłuższego wspólnego prefiksu sufiksów jednego
kubełka
+ nie przekracza $L$, to uporządkowywane są one efektywnym algorytmem
+ sortowania ciągu znaków (\emph{multikey quicksort}).
+\end{enumerate}
+
+
+\section{Algorytm \emph{two-stage}}
+
+Hideo Itoh i~Hozumi Tanaka zaproponowali w~pracy \cite{IT} algorytm tworzenia
+tablic sufiksów o~nazwie \emph{two-stage}. Algorytm ten dzieli sufiksy na dwie
+kategorie: sufiksy typu $A$ to wszystkie sufiksy $S_i$ spełniające
nierówność $x[i] > x[i+1]$,
+sufiksy typu $B$ to sufiksy spełniające nierówność $x[i] \leq x[i+1]$.
+
+Algorytm rozpoczyna swoje działanie od obliczenia \SA{1}. Początek i~koniec
+każdej grupy zapamiętywany jest w~tablicach $\mathit{head}$
i~$\mathit{tail}$. Długość tych tablic odpowiada wielkości słownika
symboli.
+Sufiksy w~każdej \emph{1-grupie} są uporządkowywane w~taki sposób, żeby
sufiksy typu $A$
+były przed sufiksami typu $B$. Wynika to z~tego, że jeżeli sufiksy $S_i$
typu $A$ i~$S_j$ typu $B$ mają wspólny prefiks długości jednego symbolu, to
sufiks $S_i$ poprzedza sufiks $S_j$ w~porządku leksykograficznym. Indeksy
pierwszych sufiksów typu $B$ każdej
+grupy zapamiętywane są w~tablicy $\mathit{part}$ długości $\sigma$.
+Kolejnym krokiem algorytmu jest sortowanie sufiksów typu $B$ wewnątrz każdej
+grupy. Autorzy pracy \cite{IT} sugerują użycie do tego celu algorytmu
+\cite{bentley}, nie jest to jednak konieczne i~można do tego celu użyć
innego
+algorytmu sortowania ciągów znaków.
+
+
+Następnie ustalany jest porządek sufiksów typu $A$. Tablica \SA{}
przeglądana
+jest od lewej do prawej, znajdując wartości $i=\mathit{SA}[j],
j=0,1,\ldots,n-1$. Jeżeli
+$S_{i-1}$ jest jeszcze nieuporządkowanym sufiksem typu $A$, to umieszczany
jest
+na początku grupy do której należy. Odpowiednia wartość w~tablicy
\emph{head} jest potem
+inkrementowana. Po jednokrotnym przejrzeniu \SA{} sufiksy są już w~pełni
+posortowane, co kończy algorytm (przykład na rysunku~\ref{rys:it}).
+
+\begin{figure}[ht]
+ \begin{center} \small
+ \begin{tabular}{r c c c c c c c c c c c c l}
+ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11
\\ \cmidrule{2-13}
+ $x$ = [ & b & a & d & d & a & d & d & a & c & c & a &
+ $\dollar$ & ] \\ type = [ & A & B & B & A & B & B & A & B & B
& A & A & B & ] \\ \addlinespace[1em]
+
+ \multicolumn{14}{c}{\emph{1-sort}}\\
+ \SA{} = [ & 11 & (-- & 1 & 4 & 7) & (--) & (-- & 8) & (-- & -- & 2 &
5) & ] \\
+ type = [ & B & A & B & B & B & A & A & B & A & A & B & B
& ] \\ \addlinespace[1em]
+
+ \multicolumn{14}{c}{sortowanie sufiksów typu $B$} \\
+ \SA{} = [ & 11 & (-- & 7 & 4 & 1) & (--) & (-- & 8) & (-- & -- & 5 &
2) & ] \\ \addlinespace[1em]
+
+ \multicolumn{14}{c}{wstawianie sufiksów typu $A$}\\
+ \SA{} = [ & 11 & 10 & 7 & 4 & 1 & -- & -- & 8 & -- & -- & 5 &
2 & ] \\
+ \SA{} = [ & 11 & 10 & 7 & 4 & 1 & -- & 9 & 8 & -- & -- & 5 & 2
& ] \\
+ \SA{} = [ & 11 & 10 & 7 & 4 & 1 & -- & 9 & 8 & 6 & -- & 5 & 2
& ] \\
+ \SA{} = [ & 11 & 10 & 7 & 4 & 1 & -- & 9 & 8 & 6 & 3 & 5 & 2
& ] \\
+ \SA{} = [ & 11 & 10 & 7 & 4 & 1 & 0 & 9 & 8 & 6 & 3 & 5 & 2
& ] \\
+ \end{tabular}
+ \end{center}
+ \caption{Przebieg algorytmu \emph{two-stage} dla słowa ,,baddaddacca''.
+ Nieuporządkowane sufiksy typu $A$ oznaczane są znakiem ,,--''. Źródło:
+ opracowanie własne na podstawie \cite{taxonomy}.}%
+ \label{rys:it}
+\end{figure}
+
+
+\section{Algorytm \emph{improved two-stage}}
+
+Algorytm \emph{improved two-stage} opisany został w~pracy \cite{MP}, której
+autorami są Simon Puglisi i~Michael Maniscalco.
+Kwestia autorstwa tego algorytmu pozostaje niejasna, metoda ta posiada aż trzy
niezależne
+implementacje powstałe przed publikacją artykułu:
+\begin{itemize}
+ \item \emph{archon } [\ref{archon}] autorstwa Dimy Małyszewa,
+ \item \emph{divsufsort} [\ref{libdivsufsort}] której autorem jest Yuta Mori,
+ \item \emph{msufsort} [\ref{msufsort}] autorstwa Michaela Maniscalco.
+\end{itemize}
+Wymienione implementacje algorytmu \emph{improved two-stage} napisane zostały
w~języku \texttt{C++}.
+
+Na początku sufiksy są dzielone na dwie kategorie: sufiksy typu $A$ to
sufiksy
+$S_i$ spełniające nierówność $S_i > S_{i+1}$, sufiksy typu $B$ to sufiksy
+spełniające nierówność $S_i \leq S_{i+1}$. Sufiks o~identyfikatorze $n-1$
należy
+do obu grup. Następnie, sufiksy $S_i$ typu $B$ których następny sufiks
$S_{i+1}$ jest typu $A$ oznaczane są jako
+sufiksy typu $B^*$.
+
+Kolejnym krokiem algorytmu jest znalezienie granic grup które powstałyby po
+\emph{2-sortowaniu}. Następnie tworzony jest \emph{2-porządek} sufiksów typu
+$B^*$. \emph{2-sortowanie} wszystkich sufiksów nie jest konieczne w~tym
+momencie, a~jego pominięcie zmniejsza czas działania algorytmu.
+Sufiksy typu $B^*$ należące do jednej grupy są sortowane zgodnie z~metodami
+przedstawionymi w~pracach \cite{bentley, MF} i~umieszczane na początkowych
+pozycjach wewnątrz kubełka w~tablicy \SA{}.
+
+Porządek sufiksów typu $B$ ustalany jest poprzez przeglądanie tablicy \SA{}
od
+prawej do lewej. Dla każdego sufiksu $\mathit{SA}[i]$ odczytanego podczas
+przeglądania tablicy sufiks $\mathit{SA}[i]-1$ jest wstawiany na ostatnią
pustą
+pozycję wewnątrz swojej grupy jeżeli jest sufiksem typu $B$.
+
+Wstawianie sufiksów typu $A$ wykonywane jest w~sposób identyczny jak
w~algorytmie
+\emph{two-stage} (przykład przedstawiono na rysunku \ref{rys:div}).
+
+\begin{figure}[t]
+ \begin{center}\small
+ \begin{tabular}{r c c c c c c c c c c c c c c l}
+ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 &
10 & 11 & 12 & 13 \\\cmidrule{2-15}
+ $x$ = [ & e & d & a & b & d & c & c & d & e & e &
+ d & a & b & $\dollar$ & ] \\ type = [ & A & A & B & $B^*$
& A & B & B & $B^*$ & A & A & A & $B^*$ & A & & ] \\
\addlinespace[1em]
+ \multicolumn{16}{c}{Obliczanie wielkości \emph{2-grup}}\\
+ \SA{2} = [ & -- & (-- & --) & -- & -- & -- & -- & (-- & --) &
-- & -- & (-- & --) & -- & ] \\ \addlinespace[1em]
+ \multicolumn{16}{c}{Sortowanie sufiksów typu $B^*$} \\
+ \SA{} = [ & -- & 11 & -- & -- & 3 & -- & -- & -- & --
& -- & 7 & -- & -- & -- & ] \\ \addlinespace[1em]
+ \multicolumn{16}{c}{Wstawianie sufiksów typu B}\\
+ \SA{} = [ & -- & 11 & -- & -- & 3 & -- & 6 & -- & -- &
-- & 7 & -- & -- & -- & ] \\
+ \SA{} = [ & -- & 11 & -- & -- & 3 & 5 & 6 & -- & -- &
-- & 7 & -- & -- & -- & ] \\
+ \SA{} = [ & -- & 11 & 2 & -- & 3 & 5 & 6 & -- & -- &
-- & 7 & -- & -- & -- & ] \\ \addlinespace[1em]
+ \multicolumn{16}{c}{Wstawianie sufiksów typu A}\\
+ \SA{} = [ & 13 & 11 & 2 & -- & 3 & 5 & 6 & -- & -- & --
& 7 & -- & -- & -- & ] \\
+ \SA{} = [ & 13 & 11 & 2 & 12 & 3 & 5 & 6 & -- & -- & --
& 7 & -- & -- & -- & ] \\
+ \SA{} = [ & 13 & 11 & 2 & 12 & 3 & 5 & 6 & 10 & -- & --
& 7 & -- & -- & -- & ] \\
+ \SA{} = [ & 13 & 11 & 2 & 12 & 3 & 5 & 6 & 10 & 1 & -- &
7 & -- & -- & -- & ] \\
+ \SA{} = [ & 13 & 11 & 2 & 12 & 3 & 5 & 6 & 10 & 1 & 4 &
7 & -- & -- & -- & ] \\
+ \SA{} = [ & 13 & 11 & 2 & 12 & 3 & 5 & 6 & 10 & 1 & 4 &
7 & 9 & -- & -- & ] \\
+ \SA{} = [ & 13 & 11 & 2 & 12 & 3 & 5 & 6 & 10 & 1 & 4 &
7 & 9 & 0 & -- & ] \\
+ \SA{} = [ & 13 & 11 & 2 & 12 & 3 & 5 & 6 & 10 & 1 & 4 &
7 & 9 & 0 & 8 & ] \\
+ \end{tabular}
+ \end{center}
+ \caption{Przebieg algorytmu \emph{divsufsort} dla słowa ,,edabdccdeedab''.
+ Źródło: opracowanie własne na podstawie \cite{div}.}%
+ \label{rys:div}
+\end{figure}
+
+
+\section{Algorytm \emph{bpr}}
+
+Klaus-Bernd Schürmann w~pracy \cite{schurmann-phd} zaproponował algorytm
+\emph{bpr} (\emph{bucket pointer refinement}, polepszanie wskaźników na
+kubełki). Algorytm ten jest poprawioną wersją metody przedstawionej w~pracy
+\cite{bpr-old} napisanej przez Klausa-Bernda Schürmanna i~Jensa Stoye. Kod
+algorytmu \emph{bpr} w~języku \texttt{C++} dostępny jest na stronie
[\ref{bpr-code}].
+
+Pierwszym krokiem algorytmu jest posortowanie sufiksów według $q$-pierwszych
+znaków, czyli \emph{q-sortowanie}. Wartość parametru $q$ obliczana jest na
+podstawie liczby różnych symboli (czyli wielkości alfabetu) w~ciągu
wejściowym, jej wartość maleje wraz ze
+wzrostem wielkości słownika sekwencji wejściowej. Następnie obliczana jest
+przybliżona odwrotna tablica sufiksów \ISA{} (kubełki identyfikowane są
pozycją
+ich ostatniego elementu w~przybliżonej tablicy sufiksów), nazywana w~pracy
+\cite{schurmann-phd} \emph{tablicą wskaźników na kubełki}.
+
+Algorytm \emph{bpr} działa według schematu \emph{polepszania kubełków
wgłąb} i~korzysta z~techniki \emph{pull}. Sufiksy $S_i$ i~$S_j$ należące
+do jednej \emph{h-grupy} porównywane są poprzez porównanie wartości
+\ISA{}$[h + i]$ i~\ISA{}$[h + j]$.
+
+Każda ze znalezionych na początku grup sortowana jest algorytmem
\emph{ternary
+split quicksort} \cite{bentley-sort}. Parametr $h$ przyjmuje początkowo
+wartość $q$. Algorytm ten wybiera jeden z~sufiksów danej grupy jako element
+osiowy (\english{pivot}) $S_p$ o~wartości klucza $K_p = \textit{ISA}[h + p]$.
Sufiksy danej grupy dzielone są na trzy
+podgrupy: sufiksy o~wartości klucza mniejszej, równej lub większej niż
$K_p$.
+Każda z~tych podgrup jest następnie w~ten sam sposób sortowana, przy czym
+dla grupy sufiksów o~wartości klucza równej elementowi osiowemu wartość
+parametru $h$ zwiększana jest o~$q$, ponieważ wszystkie jej sufiksy mają
+wspólny prefiks długości $h + q$. Wynika to z~tego, że elementy kubełka
o~wspólnym prefiksie długości $h$ sortowane są na podstawie pozycji ich
+\emph{h-następników}, dla których nie znamy długości wspólnego prefiksu.
+Wiadomo tylko tyle, że były posortowane na początku działania algorytmu
według
+$q$ pierwszych znaków. Podobnie jak w~algorytmie \emph{qsufsort}, równa
wartość
+klucza $\textit{ISA}[h + i]$ i~$\textit{ISA}[h + j]$ oznacza że sufiksy $S_i$
i~$S_j$ mają wspólny prefiks długości $h+q$. Fundamentalna różnica między
+algorytmami \emph{bpr} i~\emph{qsufsort} polega na tym, że pierwszy z~nich
+realizuje schemat \emph{polepszania kubełków wgłąb}, a~drugi
\emph{polepszania
+wszerz}. Dzięki temu, algorytm \emph{qsufsort} w~kolejnej iteracji może
+podwajać wartość parametru $h$.
+
+Istotną cechą algorytmu \emph{bpr} jest to, że po każdym podziale grupy na
+podgrupy wykonywana jest aktualizacja wpisów w~tablicy \ISA{} odpowiadających
+jej elementom, zgodnie ze wzorem $\textit{ISA}[i] =$ \emph{pozycja
+ostatniego elementu podgrupy}. Na rysunku \ref{rys:bpr} przedstawiony został
+przebieg działania algorytmu \emph{bpr} na przykładzie ciągu ,,DEBDEBDEA''.
+
+\begin{figure}[t]
+ \begin{center}\small
+ \begin{tabular}{r c c c c c c c c c l}
+ & 0 & 1 & 2 & 3 & 4
& 5 & 6 & 7 & 8 & \\ \cmidrule{2-10}
+ $x=[$ & D & E & B & D & E
& B & D & E & A & ] \\
\addlinespace[.5em]
+ \multicolumn{11}{c}{Podział
na kubełki, $q=2$} \\
+ & A & \multicolumn{2}{c}{BD} &
\multicolumn{3}{c}{DE} & EA & \multicolumn{2}{c}{EB} & \\
+ $\textit{SA}=[$ & 8 & \textbf{(2} & \textbf{5)} & (0 & 3
& 6) & 7 & (1 & 4) & $]$ \\
+ $\textit{ISA}=[$ & 5 & 8 & 2 & 5 &
\textbf{8} & 2 & 5 & \textbf{6} & 0 & $]$ \\
\addlinespace[.5em]
+ \multicolumn{11}{c}{Po
posortowaniu kubełka BD} \\
+ $\textit{SA}=[$ & 8 & 5 & 2 & \textbf{(0} &
\textbf{3} & \textbf{6)} & 7 & (1 & 4) & $]$ \\
+ $\textit{ISA}=[$ & 5 & 8 & \textbf{2} & 5 & 8
& \textbf{1} & 5 & 6 & \textbf{0} & $]$ \\
\addlinespace[.5em]
+ \multicolumn{11}{c}{Po
posortowaniu kubełka DE} \\
+ $\textit{SA}=[$ & 8 & 5 & 2 & 6 & 3
& 0 & 7 & \textbf{(1} & \textbf{4)} & $]$ \\
+ $\textit{ISA}=[$ & 5 & 8 & 2 & \textbf{4} & 8
& 1 & \textbf{3} & 6 & 0 & $]$ \\
\addlinespace[.5em]
+ \multicolumn{11}{c}{Po posortowaniu
kubełka EB, koniec algorytmu} \\
+ $\textit{SA}=[$ & 8 & 5 & 2 & 6 & 3
& 0 & 7 & 4 & 1 & $]$ \\
+ $\textit{ISA}=[$ & 5 & 8 & 2 & 4 & 7
& 1 & 3 & 6 & 0 & $]$ \\
+ \end{tabular}
+ \end{center}
+
+ \caption{Przebieg algorytmu \emph{bpr} dla słowa ,,DEBDEBDEA''. Elementy
+ wyróżnione w~tablicy \emph{SA} przeznaczone do uporządkowania w~danym
+ kroku, elementy wyróżnione w~tablicy \ISA{} to klucze wykorzystywane
+ do sortowania kubełka. Źródło: opracowanie własne na podstawie
+ \cite{schurmann-phd}.}\label{rys:bpr}
+\end{figure}
+
Added: trunk/templates/example-msc-polish/05-testy.tex
==============================================================================
--- (empty file)
+++ trunk/templates/example-msc-polish/05-testy.tex Tue Oct 13 10:21:45 2009
@@ -0,0 +1,442 @@
+\chapter{Testy wydajnościowe}
+
+\section{Wstęp}
+
+W~poniższym rozdziale przedstawione zostaną wyniki testów wydajnościowych
implementacji algorytmów
+opisanych w~poprzedniej części pracy (poza algorytmem \emph{two-stage},
który został rozwinięty
+i~poprawiony przez \emph{improved two-stage}). Implementacja w~języku
\texttt{Java} została oparta
+o~oryginalny kod, udostępniony przez autorów. Podstawą implementacji metody
\emph{improved
+two-stage} był kod algorytmu \emph{divsufsort} napisany przez Yutę Moriego
[\ref{libdivsufsort}].
+
+Algorytmy tworzenia tablic sufiksów zaimplementowane zostały w~ten sposób,
żeby na wejściu
+przyjmowały sekwencje liczb całkowitych typu \texttt{int} zajmujących
w~języku \texttt{Java} 4
+bajty. Spowodowało to zwiększenie złożoności pamięciowej algorytmów
(wartości podane w~tabeli
+\ref{tab:alg} zakładały wejście w~postaci sekwencji jednobajtowych
elementów). Powodem zwiększenia
+rozmiaru pojedynczego elementu wejściowego było umożliwienie tworzenia
tablic sufiksów dla sekwencji
+symboli z~alfabetów o~dużym rozmiarze. Nie jest to jednak możliwe w~praktyce
w~przypadku wszystkich
+algorytmów; rzeczywista złożoność pamięciowa implementacji wybranych
metod oraz ich zależność od
+rozmiaru alfabetu wejściowego opisane zostały w~tabeli \ref{tab:alg-impl}.
Testowane implementacje
+algorytmów \emph{bpr}, \emph{deep-shallow} i~\emph{qsufsort} dla
zaoszczędzenia pamięci nadpisywały
+ciąg wejściowy. Na potrzeby testów wydajnościowych zaimplementowano
również naiwny algorytm
+tworzenia tablic sufiksów opierający się o~zwykły algorytm sortujący
\emph{quicksort}. W~dalszej
+części rozdziału metoda naiwna nazywana będzie \emph{naive sort} lub NS.
+
+Wykonane testy algorytmów można podzielić na dwie główne kategorie: testy
na wejściu generowanym
+losowo, oraz testy na wejściu wczytywanym z~plików. Testy drugiego typu
wykonywane były na kilku
+różnych maszynach wirtualnych:
+
+\begin{itemize}
+ \item maszyna Java HotSpot 64-Bit Server VM 11.0-b16 firmy Sun
Microsystems, oznaczana w~dalszej części pracy jako \texttt{sun},
+ \item maszyna IBM J9 VM 2.4 firmy IBM, oznaczana w~dalszej części pracy
jako \texttt{ibm},
+ \item BEA JRockit(R) R27.5.0-110\_o-99226-1.6.0\_03 firmy BEA (aktualnie
przejęta przez Oracle), oznaczana w~dalszej części pracy jako
\texttt{jrockit},
+ \item Apache Harmony DRLVM 11.2.0 tworzona przez Apache Software
Foundation, oznaczana w~dalszej części pracy jako \texttt{harmony}.
+\end{itemize}
+
+\begin{table}[ht]
+ \begin{center}
+ \begin{tabular}{l r r}
+ \toprule
+ Nazwa & Złożoność pamięciowa \\
+ \midrule
+ \emph{skew} & $16n$ \\
+ \emph{bpr} & $4|\Sigma|^3+12n$ \\
+ \emph{deep-shallow} & $4|\Sigma|^2+(x+8)n$ \\
+ \emph{divsufsort} & $4|\Sigma|^2+8n$ \\
+ \emph{qsufsort} & $8n$ \\
+ \emph{naive sort} & $8n$ \\
+ \bottomrule
+ \end{tabular}
+ \end{center}
+ \caption{Zaimplementowane algorytmy tworzenia tablic sufiksów. Parametr
$n$ oznacza długość wejścia,
+ parametr $|\Sigma|$ oznacza wielkość alfabetu sekwencji wejściowej.
Algorytm \emph{deep-shallow} wymaga
+ alfabetu o~rozmiarze nie większym niż 256, zużycie pamięci przez ten
+ algorytm zależy od wielkości budowanego drzewa \emph{blind trie}, które
maksymalnie może zawierać $n$ elementów. Rozmiar jednego elementu drzewa
wynosi $x=48$ bajtów na 64-bitowej maszynie wirtualnej firmy Sun.
+ Algorytmy \emph{bpr} i~\emph{divsufsort} nie mają sztywnych ograniczeń na
rozmiar
+ alfabetu, ale ze względu na wydajność nie powinny być używane na
dużych alfabetach.}%
+ \label{tab:alg-impl}
+\end{table}
+
+\noindent
+Testy przeprowadzone zostały na kilku komputerach testowych o~następujących
parametrach:
+\begin{itemize}
+ \item dwurdzeniowy procesor Athlon 5200 o~prędkości 2.6 GHz, 64-bitowy
system operacyjny OpenSuSE, jądro w~wersji 2.6.22.19-0.2-default,
+ \item czterordzeniowy procesor Intel Xeon x3230 o~prędkości 2.66 GHz,
64-bitowy system operacyjny OpenSuSE, wersja jądra 2.6.22.19-0.2-default,
+ \item jednordzeniowy Intel Pentium 4 o~prędkości 3 GHz, 32-bitowy system
operacyjny Windows XP.
+\end{itemize}
+
+\noindent
+Wszystkie obliczenia przeprowadzone zostały z~parametrami maszyn wirtualnych
+odpowiadającym opcjom ,,\texttt{-Xmx2g -server}'' -- zwiększają one
maksymalny rozmiar
+sterty do 2Gb, a~maszyna wirtualna pracuje w~trybie ,,serwerowym'' (agresywna
optymalizacja JIT).
+
+Czas działania algorytmów mierzony był przez klasę uruchamiającą testy,
poprzez liczenie różnicy
+wartości zwracanych przez metodę \texttt{System.currentTimeMillis()} przed
i~po obliczeniach
+(tzw.~\emph{wall time}). Do mierzenia zużycia pamięci wykorzystano specjalnie
w~tym celu napisany
+aspekt [\ref{aspectj}]. Mierzone było zużycie pamięci wewnątrz wirtualnej
maszyny na początku
+działania algorytmu, pod jego koniec oraz po zakończeniu wybranych metod
wewnątrz klas. Mierzenie
+zużycia pamięci w~języku \texttt{Java} jest trudne, bowiem maszyna wirtualna
nie pozwala na dokładne
+oszacowanie wszystkich dokonanych alokacji pamięci. Do celów testowych
posłużono się programowaniem
+aspektowym i~,,wpleciono'' (\english{code weaving}) dynamiczne instrukcje
mierzące różnicę
+w~aktualnej ilości zaalokowanej pamięci względem startu algorytmu. Nie jest
to oszacowanie idealne,
+ale pozwala na zgrubne stwierdzenie ile pamięci zużywa dany algorytm.
+
+Test na jednej instancji wejścia (pliku lub wygenerowanej sekwencji
o~ustalonych parametrach)
+powtarzany był 10 razy, a~jego wynikiem jest średnia z~zebranych pomiarów.
Testy których wyniki
+zbierano poprzedzano kilkoma uruchomieniami algorytmu. Celem tego zabiegu było
wyeliminowanie błędów
+pomiarowych wynikających z~wolniejszego działania kodu, który nie został
skompilowany do kodu
+natywnego przez maszynę wirtualną. Testy na wejściu generowanym losowo były
poprzedzone 10 rundami
+,,rozgrzewki", natomiast przed testem na wejściu wczytywanym z~pliku algorytm
uruchamiany był 5
+razy.
+
+W~dalszej części rozdziału prezentowane są wyniki pochodzące z~pomiarów
na komputerze z~procesorem
+Xeon x3230. Wyniki z~pozostałych maszyn są niemal identyczne pod względem
porównywania i~rankingu
+algorytmów, dlatego też w wielu miejscach je pominięto (wszystkie wyniki są
na dołączonej do pracy
+płycie CD). Samo porównanie efektywności wykonania programów w różnych
maszynach wirtualnych
+znajduje się w rozdziale \ref{sect:vms}.
+
+
+\section{Testy wydajnościowe na losowo generowanym wejściu}
+
+Celem testów na losowo generowanym wejściu jest zbadanie rzeczywistej
zależności algorytmów od
+długości wejścia, wielkości alfabetu oraz średniego \emph{lcp} ciągu
wejściowego. Testy
+przeprowadzono tylko na jednej maszynie wirtualnej (\texttt{sun}). Ziarno
generatora liczb losowych
+otrzymywało identyczną wartość przed testem każdego algorytmu by zapewnić
powtarzalność wyników.
+
+
+\subsection{Wejście o~zmiennej długości i~stałej wielkości alfabetu}
+
+Testy algorytmów na losowym wejściu o~zmiennej długości i~stałej
wielkości alfabetu powtórzono trzy
+razy. Każdy test wykonany był dla wejścia generowanego z~alfabetu wielkości
4,100 i~255 elementów.
+Rysunek \ref{rys:random-input-lcp} przedstawia średnią wartość \emph{lcp}
generowanych ciągów
+wejściowych. Z~rysunku wynika, że wartość średniego \emph{lcp} jest mniej
więcej odwrotnie
+proporcjonalna do wielkości alfabetu.
+
+Rysunki \ref{rys:random-input-time-4} i~\ref{rys:random-input-memory-4}
przedstawiają czas działania
+algorytmów oraz zużycie pamięci dla alfabetu wielkości 4. Algorytmy
\emph{qsufsort} i~\emph{naive
+sort} uzyskały najlepszy wynik złożoności pamięciowej. Zgodnie
z~przewidywaniami, algorytmy
+\emph{skew} i~\emph{deep shallow} wypadł najgorzej w~tej kwestii. Najszybszym
algorytmem okazał się
+być algorytm \emph{bpr}. Wyraźnie wolniejsze od pozostałych algorytmów są
algorytmy \emph{skew}
+i~\emph{naive sort}.
+
+
+\begin{figure}[t]
+ \begin{center}
+
\includegraphics[width=\linewidth]{figures/results/random-input-lcp}
+ \end{center}
+ \caption{Średnie \emph{lcp} w~zależności od długości wejścia dla
alfabetów o wielkości 4, 100 i~255 symboli.}%
+ \label{rys:random-input-lcp}
+\end{figure}
+
+\begin{figure}[tp]
+ \begin{center}
+
\includegraphics[width=\linewidth]{figures/results/random-input-memory-4}
+ \end{center}
+ \caption{Zużycie pamięci w~zależności od długości wejścia
generowanego z~alfabetu wielkości 4.}%
+ \label{rys:random-input-memory-4}
+\end{figure}
+
+%TODO wyniki zuzycia pamieci przez naive sort wskazuja na zaniżone wyniki
pomiarów -- powinny być podobne wartości jak dla algorytmu qsufsort.
+\begin{figure}[tp]
+ \begin{center}
+
\includegraphics[width=\linewidth]{figures/results/random-input-time-4.pdf}
+ \end{center}
+ \caption{Czas działania algorytmów w~zależności od długości wejścia
generowanego z~alfabetu wielkości 4.}%
+ \label{rys:random-input-time-4}
+\end{figure}
+
+\begin{figure}[tp]
+ \begin{center}
+
\includegraphics[width=\linewidth]{figures/results/random-input-memory-100.pdf}
+ \end{center}
+ \caption{Zużycie pamięci w~zależności od długości wejścia
generowanego z~alfabetu wielkości 100.}%
+ \label{rys:random-input-memory-100}
+\end{figure}
+
+% nie wiem jak wyjaśnić zwiekszone zuzycie pamieci przez algorytm divsufsort
+Wyniki testów wejścia generowanego z~alfabetu wielkości 100 przedstawione
są na rysunku
+\ref{rys:random-input-time-100} i~\ref{rys:random-input-memory-100}.
+Rezultaty testu czasu działania algorytmu są niemal identyczne jak
poprzedniego. Jedyną różnicą jest
+to, że algorytm \emph{bpr} nie uzyskał najlepszego wyniku lecz znalazł się
wśród kilku algorytmów
+uzyskujących bardo dobry wynik, zajął również więcej pamięci.
+
+\begin{figure}[tp]
+ \begin{center}
+
\includegraphics[width=\linewidth]{figures/results/random-input-time-100.pdf}
+ \end{center}
+ \caption{Czas działania algorytmów w~zależności od długości wejścia
generowanego z~alfabetu wielkości 100.}%
+ \label{rys:random-input-time-100}
+\end{figure}
+
+Rysunki \ref{rys:random-input-time-255} i~\ref{rys:random-input-memory-255}
prezentują wyniki testów
+wejścia generowanego z~alfabetu wielkości 255. Wynik tego testu są również
podobne do poprzedników.
+Algorytm \emph{bpr} uzyskał jeszcze gorszy wynik niż w~poprzednich testach,
zajął więcej pamięci
+i~działał wolniej od większości algorytmów.
+
+\begin{figure}[tp]
+ \begin{center}
+
\includegraphics[width=\linewidth]{figures/results/random-input-memory-255.pdf}
+ \end{center}
+ \caption{Zużycie pamięci w~zależności od długości wejścia
generowanego z~alfabetu wielkości 255.}%
+ \label{rys:random-input-memory-255}
+\end{figure}
+
+\begin{figure}[tp]
+ \begin{center}
+
\includegraphics[width=\linewidth]{figures/results/random-input-time-255.pdf}
+ \end{center}
+ \caption{Czas działania algorytmów w~zależności od długości wejścia
generowanego z~alfabetu wielkości 255.}%
+ \label{rys:random-input-time-255}
+\end{figure}
+
+
+\subsection{Wejście o~stałej długości i~zmiennej wielkości alfabetu}
+
+Wejście generowane na potrzeby testu miało długość 5\,000\,000 elementów.
Wykres
+\ref{rys:random-alphabet-lcp} przedstawia średnie \emph{lcp} wygenerowanego
wejścia w~zależności od
+wielkości alfabetu. Wykres \ref{rys:random-alphabet-time} przedstawia czasy
działania algorytmów na
+generowanym wejściu.
+
+Wyniki testu pokazują które algorytmy zależą od średniego \emph{lcp}
i~wielkości alfabetu sekwencji
+wejściowej. Algorytm \emph{bpr} jest tego najlepszym przykładem -- im
większa jest jedna z~tych
+wartości, tym gorzej sobie radzi. Algorytm \emph{skew} uzyskuje lepsze wyniki
dla sekwencji
+o~większej wartości średniego \emph{lcp}. Pozostałe algorytmy nie wykazują
większej zależności
+pomiędzy czasem ich działania a~wielkością alfabetu i~średnim \emph{lcp}.
+
+\begin{figure}[p]
+ \begin{center}
+
\includegraphics[width=\linewidth]{figures/results/random-alphabet-lcp.pdf}
+ \end{center}
+ \caption{Średnie \emph{lcp} generowanego wejścia w~zależności od
wielkości alfabetu.}%
+ \label{rys:random-alphabet-lcp}
+\end{figure}
+
+\begin{figure}[p]
+ \begin{center}
+
\includegraphics[width=\linewidth]{figures/results/random-alphabet-time.pdf}
+ \end{center}
+ \caption{Czas działania algorytmów w~zależności od wielkości
alfabetu.}%
+ \label{rys:random-alphabet-time}
+\end{figure}
+
+
+% Flush manually before the main section.
+\FloatBarrier
+
+\section{Testy wydajnościowe na wejściu wczytywanym z~plików}
+
+Zaimplementowane algorytmy przetestowane zostały na dwóch zestawach plików
(korpusach) specjalnie
+przygotowanych do testowania algorytmów tworzenia tablic sufiksów. Pierwszy
z~nich nosi nazwę
+\texttt{Gauntlet}, powstał z~inicjatywy Michaela Maniscalco. Ideą stojącą
za stworzeniem tego
+korpusu było zebranie plików o~nietypowej strukturze w~celu testowania
algorytmów na szczególnych
+przypadkach wejścia. Wkład w~powstanie tego zbioru plików wnieśli Yuta
Mori, Simon Puglisi oraz
+Graham Houston. Korpus dostępny jest do pobrania pod adresem [\ref{gauntlet}].
+
+Drugi korpus testowy opracowany został przez Giovanniego Manziniego. W~jego
skład wchodzą
+rzeczywiste pliki o~dużym rozmiarze pochodzące z~różnych źródeł. Zestaw
plików dostępny jest do
+pobrania pod adresem [\ref{manzini-corpus}]. Tabela \ref{tab:manzini-files}
prezentuje
+charakterystykę plików obu korpusów.
+
+\begin{table}[ht]
+ \begin{center} \small
+ \begin{tabular}{l r r}
+ \toprule
+ Plik & Rozmiar & Średnie \emph{lcp} \\
\midrule
+ \texttt{abac} & 200\,000 & 99\,997 \\
+ \texttt{abba} & 10\,500\,600 & 2\,773\,939 \\
+ \texttt{book1x20} & 15\,375\,420 & 6\,938\,159 \\
+ \texttt{fib\_s14930352} & 14\,930\,352 & 3\,940\,597 \\
+ \texttt{fss10} & 12\,078\,908 & 2\,454\,179 \\
+ \texttt{fss9} & 2\,851\,443 & 579\,353 \\
+ \texttt{houston} & 3\,840\,000 & 52\,083 \\
+ \texttt{paper5x80} & 981\,924 & 239\,421 \\
+ \texttt{test1} & 2\,097\,152 & 1\,048\,064 \\
+ \texttt{test2} & 2\,097\,152 & 1\,048\,064 \\
+ \texttt{test3} & 2\,097\,152 & 984\,064 \\
+ \bottomrule
+ \end{tabular}
+ \hspace{1cm}
+ \begin{tabular}{l r r}
+ \toprule
+ Plik & Rozmiar & Średnie \emph{lcp} \\
\midrule
+ \texttt{chr22.dna} & 34\,553\,758 & 1\,979 \\
+ \texttt{etext99} & 105\,277\,340 & 1\,108 \\
+ \texttt{gcc-3.0.tar} & 86\,630\,400 & 8\,603 \\
+ \texttt{howto} & 39\,422\,105 & 267 \\
+ \texttt{jdk13c} & 69\,728\,899 & 678 \\
+ \texttt{linux-2.4.5.tar} & 116\,254\,720 & 479 \\
+ \texttt{rctail96} & 114\,711\,151 & 282 \\
+ \texttt{rfc} & 116\,421\,901 & 93 \\
+ \texttt{sprot34.dat} & 109\,617\,186 & 89 \\
+ \texttt{w3c2} & 104\,201\,579 & 42\,299 \\
+ \bottomrule
+ \\
+ \end{tabular}
+
+ \end{center}
+ \caption{Charakterystyka plików wchodzących w~skład korpusu
\texttt{Gauntlet}
+ (po lewej) i~korpusu Giovanniego Manziniego (po prawej). Rozmiar i~średnie
\emph{lcp} podano w bajtach.}%
+ \label{tab:gauntlet-files}\label{tab:manzini-files}
+\end{table}
+
+
+\subsection{Szczegółowe wyniki na maszynie wirtualnej firmy Sun}
+
+Ze względu na wysokie podobieństwo wyników, w~poniższym rozdziale
prezentowane są szczegółowe
+rezultaty tylko z~jednej maszyny wirtualnej (\texttt{sun}). Podobnie jak
w~przypadku testów na
+różnych komputerach, wyniki testów na różnych maszynach wirtualnych są
identyczne w~sensie rankingu
+algorytmów.
+
+Algorytm \emph{deep-shallow} został pominięty w~poniższych testach ze
względu na nieakceptowalnie długi
+czas działania. Testy z~jego udziałem wykazały wielokrotnie gorszy czas
działania algorytmu od
+najgorszego z~pozostałych. Również ze względu na czas działania algorytmu
pominięto metodę naiwną.
+Algorytmy \emph{skew} i~\emph{bpr} podczas przetwarzania niektórych plików
kończyły się wyjątkiem
+braku pamięci. Takie przypadki oznaczone zostały w~zestawieniach znakiem --,
błąd
+działania algorytmu na jednym z~plików danego korpusu powodował pominięcie
tej metody w~podsumowaniu
+testów na całym zbiorze plików.
+
+Wyniki testów na korpusie \texttt{The Gauntlet} przedstawione zostały
w~tabeli
+\ref{tab:sun-gauntlet}. Rysunek \ref{rys:sun-gauntlet} obrazuje porównanie
sumy czasów działania
+algorytmów na wszystkich plikach korpusu (poza tymi algorytmami, które
błędnie zakończyły
+działanie). Analogiczne wyniki testów na korpusie Giovanniego Manziniego
przedstawione są w~tabeli
+\ref{tab:sun-manzini} oraz rysunku \ref{rys:sun-manzini}. Najlepszym algorytmem
okazał się być
+\emph{qsufsort}, który uzyskał najlepszy wynik na znakomitej większości
plików. Drugie miejsce
+przypadło algorytmowi \emph{divsufsort}. Pozostałe algorytmy uzyskiwały
znacznie gorsze wyniki lub
+nie kończyły obliczeń.
+
+
+\begin{table}[ht]
+ \begin{center}
+ \input{tables/sun/gauntlet.tex}
+ \end{center}
+ \caption{Czas działania algorytmów na plikach z~korpusu
\texttt{Gauntlet}.}%
+ \label{tab:sun-gauntlet}
+\end{table}
+
+\begin{figure}[ht]
+ \begin{center}
+ \includegraphics[width=\linewidth]{figures/results/sun-gauntlet.pdf}
+ \end{center}
+ \caption{Sumaryczny czas działania algorytmów na plikach z~korpusu
\texttt{Gauntlet}.}%
+ \label{rys:sun-gauntlet}
+\end{figure}
+
+\begin{table}[ht]
+ \begin{center}
+ \input{tables/sun/manzini.tex}
+ \end{center}
+ \caption{Czas działania algorytmów na plikach z~korpusu Giovanniego
Manziniego.}%
+ \label{tab:sun-manzini}
+\end{table}
+
+\begin{figure}[ht]
+ \begin{center}
+ \includegraphics[width=\linewidth]{figures/results/sun-manzini.pdf}
+ \end{center}
+ \caption{Sumaryczny czas działania algorytmów na plikach z~korpusu
Giovanniego Manziniego.}%
+ \label{rys:sun-manzini}
+\end{figure}
+
+
+\FloatBarrier
+\subsection{Porównanie czasów działania algorytmów na różnych maszynach
wirtualnych}\label{sect:vms}
+
+Poniżej przedstawione są wyniki podsumowań czasów działania algorytmów na
korpusach testowych. Jak
+już wspomniano wcześniej, ranking algorytmów jest identyczny dla każdej
maszyny wirtualnej. Celem
+prezentowania zestawień jest znalezienie takiej maszyny wirtualnej, na której
algorytmy działają
+najszybciej. Tabele \ref{tab:manzini-vm-compare}
i~\ref{tab:gauntlet-vm-compare} zawierają czasy
+działań algorytmów na plikach z~korpusów Giovanniego Manziniego
i~\texttt{The Gauntlet}. Ze względu
+na bardzo niskie wartości odchylenia standardowego nie umieszczono go
tabelach. Wizualne porównanie
+sum tych wyników znajduje się na rysunkach \ref{rys:manzini-vm-compare}
+i~\ref{rys:gauntlet-vm-compare}.
+
+Testowane maszyny wirtualne wypadły bardzo podobnie. Na maszynie
\texttt{harmony} algorytmy działały
+wolniej, wyniki pozostałych trzech maszyn są do siebie zbliżone. Spośród
tych wyników wyróżnia się
+jednak wynik testu algorytmu \emph{divsufsort} na korpusie Manziniego
przeprowadzonego na maszynie
+wirtualnej \texttt{jrockit} -- dwukrotnie gorszy niż na pozostałych
maszynach. Wyniki w~tabeli
+\ref{tab:jrockit-manzini} pokazują wolniejsze działania algorytmu na każdym
z~plików wejściowych.
+Analiza zapisów przebiegu działania algorytmu wykazała bardzo duże
odchylenie standardowe czasu
+działania algorytmu, co sugeruje wpływ maszyny wirtualnej (\emph{JIT},
\emph{garbage
+collector}) lub jakiś inny proces obliczeniowy działające w tle
i~zaburzający pomiar czasu.
+
+\begin{table}[ht]
+ \begin{center}
+ \input{tables/gauntlet.vm.compare.tex}
+ \end{center}
+ \caption{Czasy działania algorytmów na korpusie \texttt{Gauntlet} na
różnych maszynach wirtualnych. Podane wartości wyrażone są w~sekundach.}
+ \label{tab:gauntlet-vm-compare}
+\end{table}
+
+\begin{table}[ht]
+ \begin{center}
+ \input{tables/manzini.vm.compare.tex}
+ \end{center}
+ \caption{Czasy działania algorytmów na korpusie Giovanniego Manziniego na
różnych maszynach wirtualnych. Podane wartości wyrażone są w~sekundach.}
+ \label{tab:manzini-vm-compare}
+\end{table}
+
+% TODO: kolorowe rysunki nie są dobrym pomysłem na wydruk, a te wszystkie
kolory są tak samo pastelowe i wyjdą szaro. No
+% chyba, że będziesz drukował w kolorze...
+
+\begin{figure}[p]
+ \begin{center}
+
\includegraphics[width=.9\linewidth]{figures/results/gauntlet-compare.pdf}
+ \end{center}
+ \caption{Porównanie czasu działania algorytmów na korpusie
\texttt{Gauntlet} na różnych maszynach wirtualnych.}
+ \label{rys:gauntlet-vm-compare}
+\end{figure}
+
+\begin{figure}[p]
+ \begin{center}
+
\includegraphics[width=.9\linewidth]{figures/results/manzini-compare.pdf}
+ \end{center}
+ \caption{Porównanie czasu działania algorytmów na korpusie
Giovanniego Manziniego na różnych maszynach wirtualnych.}
+ \label{rys:manzini-vm-compare}
+\end{figure}
+
+
+\FloatBarrier
+\section{Analiza wyników}
+
+Najlepszym spośród zaimplementowanych algorytmów okazał się algorytm
\emph{qsufsort}. Cechuje się on
+odpornością na specyficzne typy danych wejściowych, nie zależy w dużym
stopniu ani od rozmiaru
+alfabetu sekwencji wejściowej ani od wartości średniego \emph{lcp}.
Dodatkowym atutem jest brak
+użycia dodatkowej pamięci ponad tą wymaganą do przechowania wejścia
i~wyjścia algorytmu (oraz stosu
+zużytego podczas rekurencyjnego sortowania). Na drugim miejscu znalazł się
algorytm
+\emph{divsufsort} ustępujący zwycięzcy zarówno pod względem czasu
działania, jak i~zużycia pamięci.
+Pozostałe algorytmy wypadły dużo gorzej niż wymieniona dwójka.
+
+Co ciekawe, publikowane w~internecie wyniki testów wydajnościowych
implementacji algorytmów w~języku
+\texttt{C++} [\ref{msufsort}, \ref{mori-benchmark}] dają nieco inny obraz
rankingu tych algorytmów.
+Najlepsze wyniki uzyskują tam implementacje algorytmu \emph{improved
two-stage}, czyli
+\emph{archon}, \emph{divsufsort} i~\emph{msufsort}. Algorytm \emph{qsufsort}
uzyskuje dobre, choć
+wyraźnie gorsze wyniki. Wytłumaczenie przyczyn tego faktu leży zapewne
w~różnicach między językami
+\texttt{C++} a~\texttt{Java} (oraz działaniem kodu natywnego i~kodu
uruchamianego na maszynie
+wirtualnej). Algorytm \emph{qsufsort} jest prostym algorytmem, zarówno
koncepcyjnie jak
+i~implementacyjnie. Przepisanie go z~\texttt{C++} do \texttt{Javy} nie było
trudne. Algorytm
+\emph{divsufsort} jest dużo bardziej złożony (jego implementacja w~języku
\texttt{Java} jest o~ponad
+2000 linii kodu dłuższa od \emph{qsufsort}). Z~powodu wykorzystywania
wskaźników oraz instrukcji
+\texttt{\#define} w~oryginalnej implementacji, kod w~języku \texttt{Java}
różni się od oryginału
+w~wielu miejscach. Wydaje się, że dominujące dla szybkości działania
różnice to:
+\begin{itemize}
+ \item allokacja złożonych struktur danych (i tablic lokalnych)
następuję w języku \texttt{Java}
+ na stercie, a nie na stosie; oprócz samego narzutu allokacji dochodzi tu
również koszt
+ procesu oczyszczania pamięci (\emph{garbage collector});
+
+ \item wskaźniki z języków niskopoziomowych muszą być modelowane jako
indeksy nad tablicami typów prostych,
+ co w języku \texttt{Java} wiąże się z dodatkowym narzutem sprawdzenia
czy indeks nie przekracza
+ rozmiaru tablicy;
+
+ \item rozmiar kodu natywnego generowanego dynamicznie w języku
\texttt{Java} prawdopodobnie przekraczał wielokrotnie
+ rozmiar kodu skompilowanego w języku \texttt{C}, powodując gorsze
użytkowanie pamięci podręcznej
+ procesora.
+\end{itemize}
+
+Algorytm \emph{skew} jako jedyny spośród testowanych algorytmów posiadał
liniową teoretyczną złożoność
+obliczeniową. W~testach wydajnościowych wypadł jednak bardzo słabo,
zarówno w~testach implementacji
+w~języku \texttt{Java}, jak i~w~języku \texttt{C++}. Przyczyną takiego
zachowania algorytmu jest
+jego bardzo duża złożoność pamięciowa zwiększana dodatkowo przez
rekurencyjne wywoływanie algorytmu.
+Ponadto, rekurencja wiąże się z~dodatkowymi kosztami związanymi z~obsługą
stosu. Należy również
+pamiętać, że podane złożoności pozostałych algorytmów są wartościami
pesymistycznymi, które są
+rzadko osiągane w praktyce.
+
+
Added: trunk/templates/example-msc-polish/06-zakonczenie.tex
==============================================================================
--- (empty file)
+++ trunk/templates/example-msc-polish/06-zakonczenie.tex Tue Oct 13 10:21:45
2009
@@ -0,0 +1,29 @@
+\chapter{Podsumowanie i kierunki dalszego rozwoju}
+
+Nadrzędnym celem niniejszej pracy było napisanie (w formie biblioteki)
implementacji wybranych
+algorytmów tworzenia tablic sufiksów w celu analizy ich efektywności i
zachowania w języku wysokiego
+poziomu, jakim jest język \texttt{Java}. Zadanie to obejmowało zapoznanie
się z~dostępną literaturą
+poświęconą tematyce tablic sufiksów, wybór najciekawszych algorytmów oraz
ich opisanie. Dodatkowo,
+w~wyniku pracy powinna była powstać klasyfikacja algorytmów tworzenia tablic
sufiksów.
+
+Największym wyzwaniem podczas tworzenia pracy było znalezienie najlepszych
spośród algorytmów
+tworzenia tablic sufiksów. Bardzo pomocne były w~tym opracowania zawierające
zestawienia algorytmów
+\cite{taxonomy, schurmann-phd} oraz publikowane w~internecie wyniki testów
wydajnościowych
+[\ref{msufsort}, \ref{mori-benchmark}]. Pewnym problemem podczas implementacji
algorytmów było tłumaczenie
+do języka \texttt{Java} takich konstrukcji języka \texttt{C++}, jak
instrukcje \texttt{define},
+wskaźniki oraz inne polecenia preprocesora.
+
+Podsumowując, należy stwierdzić, że wszystkie zakładane cele zostały
zrealizowane. Przegląd
+literatury, opisy algorytmów oraz ich klasyfikacja znalazły się w~tekście
tej pracy, podobnie jak
+wyniki testów wydajnościowych powstałej implementacji. Według naszej wiedzy
niniejsza praca jest
+pierwszą publikacją w~języku polskim poświęconą w całości tematyce
algorytmów tworzenia tablic
+sufiksów. Zaimplementowana biblioteka programowa jest zaś na dzień
dzisiejszy jedyną taką pozycją
+dedykowaną algorytmom tworzenia tablic sufiksów napisaną w~języku
\texttt{Java}. Kod źródłowy
+biblioteki jest udostępniony na licencji BSD, można go pobrać ze strony
projektu:
+\url{http://www.jsuffixarrays.org}.
+
+Przewidywany dalszy rozwój biblioteki zakłada opracowanie algorytmu
dobierającego najlepszą metodę
+tworzenia tablic sufiksów na podstawie charakterystyki danych wejściowych
(rozmiaru alfabetu i
+rozkładu symboli w danych wejściowych). Interesującym kierunkiem rozwoju
biblioteki jest również
+stworzenie własnej implementacji algorytmu \emph{improved two-stage},
dostosowanej do specyfiki
+języka \texttt{Java}.
Added: trunk/templates/example-msc-polish/a1-vm.tex
==============================================================================
--- (empty file)
+++ trunk/templates/example-msc-polish/a1-vm.tex Tue Oct 13 10:21:45 2009
@@ -0,0 +1,104 @@
+
+\chapter{Wyniki dla pozostałych maszyn wirtualnych}
+
+\begin{table}[p]
+ \begin{center}
+ \input{tables/ibm/gauntlet.tex}
+ \end{center}
+ \caption{Czas działania algorytmów na plikach z korpusu \texttt{The
Gauntlet} dla maszyny wirtualnej \texttt{ibm}.}%
+ \label{tab:ibm-gauntlet}
+\end{table}
+
+\begin{figure}[p]
+ \begin{center}
+ \includegraphics[width=\linewidth]{figures/results/ibm-gauntlet.pdf}
+ \end{center}
+ \caption{Sumaryczny czas działania algorytmów na plikach z korpusu
\texttt{The Gauntlet} dla maszyny wirtualnej \texttt{ibm}.}%
+ \label{rys:ibm-gauntlet}
+\end{figure}
+
+
+\begin{table}[p]
+ \begin{center}
+ \input{tables/ibm/manzini.tex}
+ \end{center}
+ \caption{Czas działania algorytmów na plikach z korpusu Giovanniego
Manziniego dla maszyny wirtualnej \texttt{ibm}.}%
+ \label{tab:ibm-manzini}
+\end{table}
+
+\begin{figure}[p]
+ \begin{center}
+ \includegraphics[width=\linewidth]{figures/results/ibm-manzini.pdf}
+ \end{center}
+ \caption{Sumaryczny czas działania algorytmów na plikach z korpusu
Giovanniego Manziniego dla maszyny wirtualnej \texttt{ibm}.}%
+ \label{rys:ibm-manzini}
+\end{figure}
+
+
+\begin{table}[p]
+ \begin{center}
+ \input{tables/jrockit/gauntlet.tex}
+ \end{center}
+ \caption{Czas działania algorytmów na plikach z korpusu \texttt{The
Gauntlet} dla maszyny wirtualnej \texttt{jrockit}.}%
+ \label{tab:jrockit-gauntlet}
+\end{table}
+
+\begin{figure}[p]
+ \begin{center}
+
\includegraphics[width=\linewidth]{figures/results/jrockit-gauntlet.pdf}
+ \end{center}
+ \caption{Sumaryczny czas działania algorytmów na plikach z korpusu
\texttt{The Gauntlet} dla maszyny wirtualnej \texttt{jrockit}.}%
+ \label{rys:jrockit-gauntlet}
+\end{figure}
+
+
+\begin{table}[p]
+ \begin{center}
+ \input{tables/jrockit/manzini.tex}
+ \end{center}
+\caption{Czas działania algorytmów na plikach z korpusu Giovanniego
Manziniego dla maszyny wirtualnej \texttt{jrockit}.}%
+ \label{tab:jrockit-manzini}
+\end{table}
+
+\begin{figure}[p]
+ \begin{center}
+
\includegraphics[width=\linewidth]{figures/results/jrockit-manzini.pdf}
+ \end{center}
+ \caption{Sumaryczny czas działania algorytmów na plikach z korpusu
Giovanniego Manziniego dla maszyny wirtualnej \texttt{jrockit}.}%
+ \label{rys:jrockit-manzini}
+\end{figure}
+
+
+\begin{table}[p]
+ \begin{center}
+ \input{tables/harmony/gauntlet.tex}
+ \end{center}
+ \caption{Czas działania algorytmów na plikach z korpusu \texttt{The
Gauntlet} dla maszyny wirtualnej \texttt{harmony}.}%
+ \label{tab:harmony-gauntlet}
+\end{table}
+
+\begin{figure}[p]
+ \begin{center}
+
\includegraphics[width=\linewidth]{figures/results/harmony-gauntlet.pdf}
+ \end{center}
+ \caption{Sumaryczny czas działania algorytmów na plikach z korpusu
\texttt{The Gauntlet} dla maszyny wirtualnej \texttt{harmony}.}%
+ \label{rys:harmony-gauntlet}
+\end{figure}
+
+
+\begin{table}[p]
+ \begin{center}
+ \input{tables/harmony/manzini.tex}
+ \end{center}
+ \caption{Czas działania algorytmów na plikach z korpusu Giovanniego
Manziniego dla maszyny wirtualnej \texttt{harmony}.}%
+ \label{tab:harmony-manzini}
+\end{table}
+
+\begin{figure}[p]
+ \begin{center}
+
\includegraphics[width=\linewidth]{figures/results/harmony-manzini.pdf}
+ \end{center}
+ \caption{Sumaryczny czas działania algorytmów na plikach z korpusu
Giovanniego Manziniego dla maszyny wirtualnej \texttt{harmony}.}%
+ \label{rys:harmony-manzini}
+\end{figure}
+
\ No newline at end of file
Added: trunk/templates/example-msc-polish/a2-web-resources.tex
==============================================================================
--- (empty file)
+++ trunk/templates/example-msc-polish/a2-web-resources.tex Tue Oct 13 10:21:45
2009
@@ -0,0 +1,56 @@
+\chapter*{Zasoby internetowe}\label{sect:web-resources}%
+\phantomsection\addcontentsline{toc}{chapter}{Zasoby internetowe}
+
+\newcommand{\tturl}{\begingroup \urlstyle{tt}\Url}
+
+{\small
+\begin{enumerate}[{[}A{]}]
+ \item \label{hart} Project Gutenberg. \\
+ \tturl{http://www.gutenberg.net}
+ \item \label{aspectj} The AspectJ Project. \\
+ \tturl{http://www.eclipse.org/aspectj/}
+ \item \label{gauntlet} The Gauntlet (Universal Robustness Corpus). \\
+ \tturl{http://www.michael-maniscalco.com/testset/gauntlet/}
+ \item \label{manzini-corpus} Manzini's Large Corpus. \\
+ \tturl{http://www.mfn.unipmn.it/~manzini/lightweight/corpus/}
+ % \item \label{carrot} Carrot2 Clustering Engine. \\
+ % \tturl{http://carrot2.org/}
+ % \item \label{jsa} Java Suffix Arrays. \\
+ % \tturl{http://jsuffixarrays.org/}
+ % \item \label{bsd} New BSD License \\
+ % \tturl{http://www.opensource.org/licenses/bsd-license.php}
+
+
+ \item \label{mori-benchmark} Yuta Mori, Suffix Array Construction Benchmark
\\
+ \tturl{http://homepage3.nifty.com/wpage/benchmark/index.html}
+
+ \item \label{msufsort} Michael Maniscalco, The MSufSort Algorithm. \\
+ \tturl{http://www.michael-maniscalco.com/msufsort.htm}
+
+ \item \label{KScode} Peter Sanders, Skew algorithm. \\
+ \tturl{http://www.mpi-inf.mpg.de/~sanders/programs/suffix/}
+
+
+ \item \label{ssort} M. Douglas McIlroy, ssort.c \\
+ \tturl{http://cm.bell-labs.com/cm/who/doug/source.html}
+
+ \item \label{archon} Dmitry A. Malyshev, Archon \\
+ \tturl{http://kvgate.com/index.php?root/comp/arch/archon/}
+
+ \item \label{MFcode} Giovanni Manzini, A Lightweight Suffix Array and BWT
Construction Algorithm \\
+ \tturl{http://web.unipmn.it/~manzini/lightweight/ds.tgz}
+
+ \item \label{libdivsufsort} Yuta Mori, libdivsufsort project homepage. \\
+ \tturl{http://code.google.com/p/libdivsufsort/}
+
+
+ \item \label{LScode} N.Jesper Larsson, qsufsort.c \\
+ \tturl{http://www.larsson.dogma.net/qsufsort.c}
+
+\item \label{bpr-code} Klaus-Bernd Sch\"{u}rmann i Jens Stoye, bpr
downloadpage. \\
+ \tturl{http://bibiserv.techfak.uni-bielefeld.de/download/tools/bpr.html}
+
+
+
+\end{enumerate}
+}
Added: trunk/templates/example-msc-polish/bibliography.bib
==============================================================================
--- (empty file)
+++ trunk/templates/example-msc-polish/bibliography.bib Tue Oct 13 10:21:45 2009
@@ -0,0 +1,433 @@
+@book{gusfield,
+ author = {Gusfield, Dan },
+ howpublished = {Hardcover},
+ isbn = {0521585198},
+ keywords = {algorithms, matching, pattern},
+ month = {styczeń},
+ posted-at = {2006-05-24 13:48:58},
+ priority = {2},
+ publisher = {{Cambridge University Press}},
+ title = {Algorithms on Strings, Trees, and Sequences: Computer Science and
Computational Biology},
+ url =
{http://www.amazon.ca/exec/obidos/redirect?tag=citeulike09-20\&path=ASIN/052\
1585198},
+ year = {1997}
+}
+
+@article{taxonomy,
+ address = {New York, NY, USA},
+ author = {Puglisi, Simon J. and Smyth, William. F. and Turpin, Andrew
H. },
+ doi = {http://dx.doi.org/10.1145/1242471.1242472},
+ issn = {0360-0300},
+ journal = {ACM Comput. Surv.},
+ keywords = {suffix-array},
+ number = {2},
+ posted-at = {2008-11-05 13:43:45},
+ priority = {3},
+ publisher = {ACM Press},
+ title = {A taxonomy of suffix array construction algorithms},
+ volume = {39},
+ year = {2007}
+}
+
+@misc{lcp-kasai,
+ author = {Toru Kasai and Hiroki Aftmura and Setsue Arikawa},
+ title = {Efficient Substring Traversal with Suffix Arrays},
+ year = {2001}
+}
+
+@article{lcp-manzini,
+ author = {Manzini, Giovanni },
+ citeulike-article-id = {3790358},
+ journal = {Algorithm Theory - SWAT 2004},
+ pages = {372--383},
+ posted-at = {2008-12-15 22:38:25},
+ title = {Two Space Saving Tricks for Linear Time LCP Array Computation},
+ url = {http://www.springerlink.com/content/tnmt7tct6aw188v0},
+ year = {2004}
+}
+
+@phdthesis{ larsson99structures,
+ author = "Jessper N. Larsson",
+ title = "Structures of String Matching and Data Compression",
+ school = "Department of Comp. Science, Lund University",
+ year = "1999",
+}
+
+@phdthesis{ schurmann-phd,
+ author = "Klaus-Bernd Schürmann",
+ title = "Suffix Arrays in Theory and Practice",
+ school = "Faculty of Technology of Bielefeld University, Germany",
+ year = "2007",
+}
+
+@article{bpr-old,
+ author = {Sch\"{u}rmann, Klaus-Bernd and Stoye, Jens},
+ title = {An incomplex algorithm for fast suffix array construction},
+ journal = {Softw. Pract. Exper.},
+ volume = {37},
+ number = {3},
+ year = {2007},
+ issn = {0038-0644},
+ pages = {309--329},
+ doi = {http://dx.doi.org/10.1002/spe.v37:3},
+ publisher = {John Wiley \& Sons, Inc.},
+ address = {New York, NY, USA},
+ }
+
+
+@book{pknuthv3,
+ author="Donald E.~Knuth",
+ title="Sztuka programowania (Tom 3, Sortowanie i wyszukiwanie)",
+ publisher="Wydawnictwa Naukowo Techniczne, Warszawa",
+ year="2002"
+}
+
+
+
+@article{ukkonen,
+ author = {Ukkonen, Esko },
+ citeulike-article-id = {707616},
+ journal = {Algorithmica},
+ keywords = {data, structures},
+ number = {3},
+ pages = {249--260},
+ posted-at = {2006-06-22 19:34:36},
+ title = {On-Line Construction of Suffix Trees},
+ url = {http://citeseer.ist.psu.edu/ukkonen95line.html},
+ volume = {14},
+ year = {1995}
+}
+@article{mccreight,
+ address = {New York, NY, USA},
+ author = {McCreight, Edward M. },
+ citeulike-article-id = {606342},
+ doi = {http://dx.doi.org/10.1145/321941.321946},
+ issn = {0004-5411},
+ journal = {J. ACM},
+ keywords = {algorithm},
+ month = {kwiecień},
+ number = {2},
+ pages = {262--272},
+ posted-at = {2006-04-29 16:03:08},
+ publisher = {ACM Press},
+ title = {A Space-Economical Suffix Tree Construction Algorithm},
+ url = {http://dx.doi.org/10.1145/321941.321946},
+ volume = {23},
+ year = {1976}
+}
+
+@inproceedings{weiner,
+ address = {Washington, DC, USA},
+ author = {Weiner, Peter },
+ booktitle = {SWAT '73: Proceedings of the 14th Annual Symposium on
Switching and Automata Theory (swat 1973)},
+ citeulike-article-id = {3817003},
+ doi = {http://dx.doi.org/10.1109/SWAT.1973.13},
+ pages = {1--11},
+ posted-at = {2008-12-22 13:25:45},
+ publisher = {IEEE Computer Society},
+ title = {Linear pattern matching algorithms},
+ url = {http://dx.doi.org/10.1109/SWAT.1973.13},
+ year = {1973}
+}
+
+@article{from-ukkonen,
+ author = {Giegerich, Robert and Kurtz, Stefan },
+ citeulike-article-id = {230069},
+ journal = {Algorithmica},
+ keywords = {stringology, suffix, trees},
+ number = {3},
+ pages = {331--353},
+ posted-at = {2005-06-16 18:30:12},
+ title = "{From Ukkonen to McCreight and Weiner}: A Unifying View of
Linear-Time Suffix Tree Construction",
+ url = {http://citeseer.ist.psu.edu/giegerich97from.html},
+ volume = {19},
+ year = {1997}
+}
+
+@inproceedings{Manber90,
+ address = {Philadelphia, PA, USA},
+ author = {Manber, Udi and Myers, Gene },
+ booktitle = {SODA '90: Proceedings of the first annual ACM-SIAM symposium on
Discrete algorithms},
+ citeulike-article-id = {221131},
+ isbn = {0898712513},
+ keywords = {ecs222a, phy250, sta232c},
+ pages = {319--327},
+ posted-at = {2005-06-07 08:42:09},
+ priority = {2},
+ publisher = {Society for Industrial and Applied Mathematics},
+ title = {Suffix arrays: a new method for on-line string searches},
+ url = {http://portal.acm.org/citation.cfm?id=320218},
+ year = {1990}
+}
+
+@article{replacing,
+ author = {Abouelhoda, Mohamed Ibrahim and Kurtz, Stefan and Ohlebusch,
Enno },
+ booktitle = {The 9th International Symposium on String Processing and
Information Retrieval},
+ citeulike-article-id = {674810},
+ doi = {http://dx.doi.org/10.1016/S1570-8667(03)00065-0},
+ journal = {Journal of Discrete Algorithms},
+ month = {marzec},
+ number = {1},
+ pages = {53--86},
+ posted-at = {2006-05-30 09:58:21},
+ priority = {3},
+ title = {Replacing suffix trees with enhanced suffix arrays},
+ url = {http://dx.doi.org/10.1016/S1570-8667(03)00065-0},
+ volume = {2},
+ year = {2004}
+
+}
+@inproceedings{abouelhoda-genome,
+ author = {Abouelhoda,, Mohamed Ibrahim and Kurtz,, Stefan and Ohlebusch,,
Enno},
+ title = {The Enhanced Suffix Array and Its Applications to Genome Analysis},
+ booktitle = {WABI '02: Proceedings of the Second International Workshop on
Algorithms in Bioinformatics},
+ year = {2002},
+ isbn = {3-540-44211-1},
+ pages = {449--463},
+ publisher = {Springer-Verlag},
+ address = {London, UK},
+ }
+
+
+@article{Ko2005,
+ author = {Ko, Pang and Aluru, Srinivas },
+ booktitle = {Combinatorial Pattern Matching (CPM) Special Issue},
+ citeulike-article-id = {2667902},
+ journal = {Journal of Discrete Algorithms},
+ keywords = {algorithms, array, biology, computational, matching, pattern,
sorting, string, suffix},
+ month = {czerwiec},
+ number = {2-4},
+ pages = {143--156},
+ pdf = {Ko2005.pdf},
+ posted-at = {2008-04-14 15:10:16},
+ priority = {2},
+ title = {Space efficient linear time construction of suffix arrays},
+ url =
{http://www.sciencedirect.com/science/article/B758J-4DB58C7-2/2/5c6103a5824f2953\
fcd05932c58946db},
+ volume = {3},
+ year = {2005}
+}
+
+@inproceedings{KS,
+ author = {K\"arkk{\"a}inen, Juha and Sanders, Peter },
+ booktitle = {Proc. 13th International Conference on Automata, Languages and
Programming},
+ citeulike-article-id = {1283587},
+ posted-at = {2007-05-08 13:49:45},
+ priority = {2},
+ publisher = {Springer},
+ title = {Simple linear work suffix array construction},
+ url = {http://citeseer.ist.psu.edu/arkk03simple.html},
+ year = {2003}
+}
+
+@TechReport{LS,
+ author = "Larsson, N. Jesper and Sadakane, Kunihiko",
+ title = "Faster Suffix Sorting",
+ institution = "Department of Computer Science, Lund University",
+ year = 1999,
+ number = "LU-CS-TR:99-214, LUNDFD6/(NFCS-3140)/1--20/(1999)",
+ address = "Sweden",
+ month = {maj}
+}
+
+
+@article{MP,
+ address = {New York, NY, USA},
+ author = {Maniscalco, Michael A. and Puglisi, Simon J. },
+ citeulike-article-id = {2898507},
+ issn = {1084-6654},
+ journal = {J. Exp. Algorithmics},
+ keywords = {array, indexing, suffix},
+ posted-at = {2008-06-16 13:33:51},
+ priority = {2},
+ publisher = {ACM},
+ title = {An efficient, versatile approach to suffix sorting},
+ url = {http://portal.acm.org/citation.cfm?id=1278374},
+ volume = {12},
+ year = {2007}
+}
+
+@misc{MF,
+ author = {Manzini, Giovanni and Ferragina, Paolo },
+ citeulike-article-id = {1638764},
+ keywords = {algorithm, pattern-matching, programming, retrieval, searching,
string, substring, text},
+ posted-at = {2007-09-09 13:17:57},
+ priority = {4},
+ title = {Engineering a lightweight suffix array construction algorithm
(Extended Abstract)},
+ url = {http://citeseer.ist.psu.edu/567924.html},
+ year = {2004}
+}
+@ARTICLE{btree,
+ author = {Paolo Ferragina and Roberto Grossi},
+ title = {The String B-Tree: A New Data Structure for String Search in
External Memory and its Applications.},
+ journal = {Journal of the ACM},
+ year = {1998},
+ volume = {46},
+ pages = {236--280}
+}
+
+
+
+
+@inproceedings{seward,
+ author = {Seward, Julian },
+ booktitle = {IEEE Data Compression Conference},
+ citeulike-article-id = {914345},
+ doi = {10.1109/DCC.2000.838157},
+ keywords = {bibtex-import, bzip2},
+ month = {marzec},
+ pages = {173--182},
+ pdf = {Seward2000pbwt.pdf},
+ posted-at = {2006-10-27 09:14:28},
+ priority = {2},
+ title = {On the Performance of BWT Sorting Algorithms},
+ year = {2000}
+ }
+
+@article{kim,
+ author = {Kim, Dong K. and Sim, Jeong S. and Park, Heejin and Park,
Kunsoo },
+ citeulike-article-id = {371055},
+ doi = {http://dx.doi.org/10.1016/j.jda.2004.08.019},
+ journal = {Journal of Discrete Algorithms},
+ keywords = {arrays, suffix},
+ month = {czerwiec},
+ number = {2-4},
+ pages = {126--142},
+ posted-at = {2005-10-30 15:24:24},
+ priority = {2},
+ title = {Constructing suffix arrays in linear time},
+ url = {http://dx.doi.org/10.1016/j.jda.2004.08.019},
+ volume = {3},
+ year = {2005}
+}
+
+@article{kim-jo-park,
+ author = {Kim, Dong K. and Jo, Junha and Park, Heejin},
+ journal = {Lecture Notes in Computer Science},
+ month = {kwiecień},
+ pages = {301-314},
+ title = {A Fast Algorithm for Constructing Suffix Arrays for Fixed-Size
Alphabets},
+ volume = {3059},
+ year = {2004}
+}
+
+@inproceedings{IT,
+ author = {Itoh,, Hideo and Tanaka,, Hozumi},
+ title = {An Efficient Method for in Memory Construction of Suffix Arrays},
+ booktitle = {SPIRE '99: Proceedings of the String Processing and Information
Retrieval Symposium \& International Workshop on Groupware},
+ year = {1999},
+ isbn = {0-7695-0268-7},
+ pages = {81},
+ publisher = {IEEE Computer Society},
+ address = {Washington, DC, USA},
+ }
+
+ @INPROCEEDINGS{Burkhardt2003,
+AUTHOR = {Burkhardt, Stefan and K{\"a}rkk{\"a}inen, Juha},
+EDITOR = {Baeza-Yates, R. and Ch{\'a}vez, E. and Crochemore, M.},
+TITLE = {Fast Lightweight Suffix Array Construction and Checking},
+BOOKTITLE = {Combinatorial Pattern Matching: 14th Annual Symposium, CPM 2003},
+PUBLISHER = {Springer},
+YEAR = {2003},
+VOLUME = {2676},
+PAGES = {55--69},
+SERIES = {Lecture Notes in Computer Science},
+ADDRESS = {Morelia, Michoacán, Mexico},
+MONTH = {czerwiec},
+ISBN = {0302-9743},
+}
+
+@ARTICLE{radix,
+ author = {Peter M. Mcilroy and Keith Bostic and M. Douglas Mcilroy},
+ title = {Engineering radix sort},
+ journal = {Computing Systems},
+ year = {1993},
+ volume = {6},
+ pages = {5--27}
+}
+
+
+
+@Misc{div,
+ author = {Mori, Yuta},
+ title = {Short description of improved two-stage suffix sorting algorithm},
+ year = {2005},
+ howpublished = "\url{http://homepage3.nifty.com/wpage/software/itssort.txt}"
+}
+
+
+@techreport{BW,
+ author = {Burrows, M. and Wheeler, D. J. },
+ citeulike-article-id = {339287},
+ number = {124},
+ posted-at = {2005-10-03 05:56:04},
+ priority = {2},
+ institution = "Digital SRC Research Report",
+ title = {A block-sorting lossless data compression algorithm.},
+ url = {http://citeseer.ist.psu.edu/76182.html},
+ year = {1994}
+}
+
+@article{bentley-sort,
+ author = {Bentley,, Jon L. and McIlroy,, M. Douglas},
+ title = {Engineering a sort function},
+ journal = {Software Practice Experience},
+ volume = {23},
+ number = {11},
+ year = {1993},
+ issn = {0038-0644},
+ pages = {1249--1265},
+ doi = {http://dx.doi.org/10.1002/spe.4380231105},
+ publisher = {John Wiley \& Sons, Inc.},
+ address = {New York, NY, USA},
+ }
+
+@inproceedings{bentley,
+ address = {Philadelphia, PA, USA},
+ author = {Bentley, Jon L. and Sedgewick, Robert },
+ booktitle = {SODA '97: Proceedings of the eighth annual ACM-SIAM symposium on
Discrete algorithms},
+ citeulike-article-id = {1574755},
+ doi = {http://dx.doi.org/10.1145/42411.42420},
+ isbn = {0898713900},
+ keywords = {balanced-tree, trie, tst},
+ pages = {360--369},
+ posted-at = {2007-08-19 07:14:21},
+ priority = {4},
+ publisher = {Society for Industrial and Applied Mathematics},
+ title = {Fast algorithms for sorting and searching strings},
+ url = {http://dx.doi.org/10.1145/42411.42420},
+ year = {1997}
+}
+
+
+@article{sinha,
+ address = {New York, NY, USA},
+ author = {Sinha, Ranjan and Zobel, Justin },
+ citeulike-article-id = {747172},
+ doi = {http://dx.doi.org/10.1145/1005813.1041517},
+ issn = {1084-6654},
+ journal = {J. Exp. Algorithmics},
+ keywords = {index\_building},
+ number = {es},
+ posted-at = {2006-07-08 10:46:56},
+ priority = {2},
+ publisher = {ACM Press},
+ title = {Cache-conscious sorting of large sets of strings with dynamic tries},
+ url = {http://dx.doi.org/10.1145/1005813.1041517},
+ volume = {9},
+ year = {2004}
+}
+
+@inproceedings{karp,
+ author = {Karp,, Richard M. and Miller,, Raymond E. and Rosenberg,, Arnold
L.},
+ title = {Rapid identification of repeated patterns in strings, trees and
arrays},
+ booktitle = {STOC '72: Proceedings of the fourth annual ACM symposium on
Theory of computing},
+ year = {1972},
+ pages = {125--136},
+ location = {Denver, Colorado, United States},
+ doi = {http://doi.acm.org/10.1145/800152.804905},
+ publisher = {ACM},
+ address = {New York, NY, USA},
+ }
+
+
+
+
\ No newline at end of file
Added: trunk/templates/example-msc-polish/figures/KS.pdf
==============================================================================
Binary file. No diff available.
Added: trunk/templates/example-msc-polish/figures/blindtrie.pdf
==============================================================================
Binary file. No diff available.
Added: trunk/templates/example-msc-polish/figures/bucket-refinement.pdf
==============================================================================
Binary file. No diff available.
Added: trunk/templates/example-msc-polish/figures/gviz.sh
==============================================================================
--- (empty file)
+++ trunk/templates/example-msc-polish/figures/gviz.sh Tue Oct 13 10:21:45 2009
@@ -0,0 +1,37 @@
+#!/bin/bash
+
+# maly skrypcik do konwersji dot i gviz'ow do PDFow. Moze sie przydac.
+
+EXT=gviz
+for i in `find . -name "*.${EXT}"`; do
+ NAME=`basename $i .${EXT}`
+ DIR=`dirname $i`
+ BASE=${DIR}/${NAME}
+
+ if [ $i -nt ${BASE}.eps ]; then
+ echo "Processing ${EXT}: " $i
+ dot -Tps -o ${BASE}.eps $i
+ cat ${BASE}.eps | gs -q -dEPSCrop -dNOCACHE -sDEVICE=epswrite
-sOutputFile=tmp - -c quit
+ mv tmp ${BASE}.eps
+ epstopdf ${BASE}.eps
+ else
+ echo "Skipping ${EXT}: " $i
+ fi
+done
+
+EXT=dot
+for i in `find . -name "*.${EXT}"`; do
+ NAME=`basename $i .${EXT}`
+ DIR=`dirname $i`
+ BASE=${DIR}/${NAME}
+
+ if [ $i -nt ${BASE}.eps ]; then
+ echo "Processing ${EXT}: " $i
+ neato -s -n2 -Tps -o ${BASE}.eps $i
+ cat ${BASE}.eps | gs -q -dEPSCrop -dNOCACHE -sDEVICE=epswrite
-sOutputFile=tmp - -c quit
+ mv tmp ${BASE}.eps
+ epstopdf ${BASE}.eps
+ else
+ echo "Skipping ${EXT}: " $i
+ fi
+done
Added: trunk/templates/example-msc-polish/figures/mississippi.gviz
==============================================================================
--- (empty file)
+++ trunk/templates/example-msc-polish/figures/mississippi.gviz Tue Oct 13
10:21:45 2009
@@ -0,0 +1,45 @@
+digraph G {
+ node [fontname=Helvetica, fontsize=12. label="", shape=point];
+ graph[page="8.5,11",size="7.5,7",ratio=fill,center=1];
+
+ rankdir=TD;
+ compound=true;
+ pack=1;
+
+ mississippi[label="mississippi", shape=ellipse]
+ ississippi[label="ississippi", shape=ellipse]
+ ssissippi[label="ssissippi", shape=ellipse]
+ sissippi[label="sissippi", shape=ellipse]
+ issippi[label="issippi", shape=ellipse]
+ ssippi[label="ssippi", shape=ellipse]
+ sippi[label="sippi", shape=ellipse]
+ ippi[label="ippi", shape=ellipse]
+ ppi[label="ppi", shape=ellipse]
+ pi[label="pi", shape=ellipse]
+ i[label="i", shape=ellipse]
+
+
+
+
+
+
+ root -> mississippi[label="mississippi"]
+ root -> i[label="i"]
+ i -> ippi[label="ppi"]
+ i -> issi[label="ssi"]
+ issi -> issippi[label="ppi"]
+ issi -> ississippi[label="ssippi"]
+
+ root -> s[label="s"]
+ s -> ss[label="s"]
+ ss -> ssippi[label="ippi"]
+ ss -> ssissippi[label="ssippi"]
+ s -> si[label="i"]
+ si -> sippi[label="ppi"]
+ si -> sissippi[label="ssippi"]
+ root -> p[label="p"]
+ p -> pi[label="i"]
+ p -> ppi[label="pi"]
+
+
+}
Added: trunk/templates/example-msc-polish/figures/mississippi.pdf
==============================================================================
Files (empty file) and
trunk/templates/example-msc-polish/figures/mississippi.pdf Tue Oct 13 10:21:45
2009 differ
Added: trunk/templates/example-msc-polish/figures/mississippi_trie.gviz
==============================================================================
--- (empty file)
+++ trunk/templates/example-msc-polish/figures/mississippi_trie.gviz Tue Oct 13
10:21:45 2009
@@ -0,0 +1,84 @@
+digraph G {
+graph[page="8.5,11",size="7.5,7",ratio=fill,center=1];
+ node [fontname=Helvetica, fontsize=12. label="", shape=point];
+
+ rankdir=TD;
+ compound=true;
+ pack=1;
+
+ mississippi[label="mississippi", shape=ellipse]
+ ississippi[label="ississippi", shape=ellipse]
+ ssissippi[label="ssissippi", shape=ellipse]
+ sissippi[label="sissippi", shape=ellipse]
+ issippi[label="issippi", shape=ellipse]
+ ssippi[label="ssippi", shape=ellipse]
+ sippi[label="sippi", shape=ellipse]
+ ippi[label="ippi", shape=ellipse]
+ ppi[label="ppi", shape=ellipse]
+ pi[label="pi", shape=ellipse]
+ i[label="i", shape=ellipse]
+
+
+
+
+
+
+ root -> m[label="m"]
+ m -> mi[label="i"]
+ mi -> mis[label="s"]
+ mis -> miss[label="s"]
+ miss -> missi[label="i"]
+ missi -> missis[label="s"]
+ missis -> mississ[label="s"]
+ mississ -> mississi[label="i"]
+ mississi -> mississip[label="p"]
+ mississip -> mississipp[label="p"]
+ mississipp -> mississippi[label="i"]
+
+ root -> i[label="i"]
+ i -> ip[label="p"]
+ ip -> ipp[label="p"]
+ ipp -> ippi[label="i"]
+
+ i -> is[label="s"]
+ is -> iss[label="s"]
+ iss -> issi[label="i"]
+ issi -> issip[label="p"]
+ issip -> issipp[label="p"]
+ issipp -> issippi[label="i"]
+ issi -> issis[label="s"]
+ issis -> ississ[label="s"]
+ ississ -> ississi[label="i"]
+ ississi -> ississip[label="p"]
+ ississip -> ississipp[label="p"]
+ ississipp -> ississippi[label="i"]
+
+ root -> s[label="s"]
+ s -> ss[label="s"]
+ ss -> ssi[label="i"]
+ ssi -> ssip[label="p"]
+ ssip -> ssipp[label="p"]
+ ssipp -> ssippi[label="i"]
+ ssi -> ssis[label="s"]
+ ssis -> ssiss[label="s"]
+ ssiss -> ssissi[label="i"]
+ ssissi -> ssissip[label="p"]
+ ssissip -> ssissipp[label="p"]
+ ssissipp -> ssissippi[label="i"]
+ s -> si[label="i"]
+ si -> sip[label="p"]
+ sip -> sipp[label="p"]
+ sipp -> sippi[label="i"]
+ si -> sis[label="s"]
+ sis -> siss[label="s"]
+ siss -> sissi[label="i"]
+ sissi -> sissip[label="p"]
+ sissip -> sissipp[label="p"]
+ sissipp -> sissippi[label="ssippi"]
+ root -> p[label="p"]
+ p -> pi[label="i"]
+ p -> pp[label="p"]
+ pp -> ppi[label="i"]
+
+
+}
Added: trunk/templates/example-msc-polish/figures/mississippi_trie.pdf
==============================================================================
Binary file. No diff available.
Added: trunk/templates/example-msc-polish/figures/reduced-string-sorting.pdf
==============================================================================
Binary file. No diff available.
Added: trunk/templates/example-msc-polish/figures/results/gauntlet-compare.pdf
==============================================================================
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Added: trunk/templates/example-msc-polish/figures/results/harmony-gauntlet.pdf
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Added: trunk/templates/example-msc-polish/graphs/readme.txt
==============================================================================
--- (empty file)
+++ trunk/templates/example-msc-polish/graphs/readme.txt Tue Oct 13 10:21:45
2009
@@ -0,0 +1,13 @@
+moim zamiarem jest stworznie DAGa, ktorego wierzcholki beda reprezentowac
algorytm wraz z jego krotkim pdsumowaniem i zrodlem, a krawedz miedzy
wierzcholkami A->B ma oznaczac "A jest cytowane w B".
+
+sam graf byc moze nie znajdzie sie w pracy, ale wydaje mi sie, ze sie przyda
przy pisaniu.
+
+% DW: Taki graf by byl super, szczegolnie jesli chodzi o drzewa sufiksowe, bo
widze, ze dla tablic to opracowanie australijczykow jest ok.
+
+do generowania grafow uzywam
+http://www.graphviz.org/
+
+% DW: no i swietnie, tak trzeba.
+
+uzycie:
+dot -Tps sample.dot -o o.ps
\ No newline at end of file
Added: trunk/templates/example-msc-polish/graphs/sample.dot
==============================================================================
--- (empty file)
+++ trunk/templates/example-msc-polish/graphs/sample.dot Tue Oct 13 10:21:45
2009
@@ -0,0 +1,49 @@
+digraph G {
+
+ node[shape=box];
+ graph[page="8.5,11",size="7.5,7",ratio=fill,center=1];
+
+ McCreight [label=<
+ <table>
+ <tr>
+ <td>E. McCreight</td>
+ <td>A space economical suffix tree construction algorithm</td>
+ </tr>
+ <tr>
+ <td colspan="2">Dodaje sufiksy wedlug rozmiaru w kolejnosci malejacej,
szybszy od Ukkonena?</td>
+ </tr>
+ </table>
+ >];
+
+ Weiner [label=<
+ <table>
+ <tr>
+ <td>P. Weiner</td>
+ <td>Linear pattern matching algorithms</td>
+ </tr>
+ <tr>
+ <td colspan="2">Od prawej do lewej, dodaje sufiksy w kolejnosci
rosnacej</td>
+ </tr>
+ </table>
+ >];
+
+ Ukkonen [label=<
+ <table>
+ <tr>
+ <td>Esko Ukkonen</td>
+ <td>On-line construction of suffix trees</td>
+ </tr>
+ <tr>
+ <td colspan="2">Pierwszy on-line</td>
+ </tr>
+ </table>
+ >];
+
+
+
+ Weiner -> Ukkonen
+ Weiner -> McCreight
+ McCreight -> Ukkonen
+
+
+}
\ No newline at end of file
Added: trunk/templates/example-msc-polish/mnowak-master-thesis.pdf
==============================================================================
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