Compressed Text Indexes:From Theory to Practice!

A compressed full-text self-index represents a text in a compressed form and still answers queries efficiently. This technology represents a breakthrough over the text indexing techniques of the previous decade, whose indexes required several times the size of the text. Although it is relatively new, this technology has matured up to a point where theoretical research is giving way to practical developments. Nonetheless this requires significant programming skills, a deep engineering effort, and a strong algorithmic background to dig into the research results. To date only isolated implementations and focused comparisons of compressed indexes have been reported, and they missed a common API, which prevented their re-use or deployment within other applications. The goal of this paper is to fill this gap. First, we present the existing implementations of compressed indexes from a practitioner's point of view. Second, we introduce the Pizza&Chili site, which offers tuned implementations and a standardized API for the most successful compressed full-text self-indexes, together with effective testbeds and scripts for their automatic validation and test. Third, we show the results of our extensive experiments on these codes with the aim of demonstrating the practical relevance of this novel and exciting technology

A representation of a compressed de Bruijn graph for pan-genome analysis that enables search

Recently, Marcus et al. (Bioinformatics 2014) proposed to use a compressed de Bruijn graph to describe the relationship between the genomes of many individuals/strains of the same or closely related species. They devised an $O(n \log g)$ time algorithm called splitMEM that constructs this graph directly (i.e., without using the uncompressed de Bruijn graph) based on a suffix tree, where $n$ is the total length of the genomes and $g$ is the length of the longest genome. In this paper, we present a construction algorithm that outperforms their algorithm in theory and in practice. Moreover, we propose a new space-efficient representation of the compressed de Bruijn graph that adds the possibility to search for a pattern (e.g. an allele - a variant form of a gene) within the pan-genome.Comment: Submitted to Algorithmica special issue of CPM201

Parallel text index construction

In dieser Dissertation betrachten wir die parallele Konstruktion von Text-Indizes. Text-Indizes stellen Zusatzinformationen über Texte bereit, die Anfragen hinsichtlich dieser Texte beschleunigen können. Ein Beispiel hierfür sind Volltext-Indizes, welche für eine effiziente Phrasensuche genutzt werden, also etwa für die Frage, ob eine Phrase in einem Text vorkommt oder nicht. Diese Dissertation befasst sich hauptsächlich, aber nicht ausschließlich mit der parallelen Konstruktion von Text-Indizes im geteilten und verteilten Speicher. Im ersten Teil der Dissertation betrachten wir Wavelet-Trees. Dabei handelt es sich um kompakte Indizes, welche Rank- und Select-Anfragen von binären Alphabeten auf Alphabete beliebiger Größe verallgemeinern. Im zweiten Teil der Dissertation betrachten wir das Suffix-Array, den am besten erforschten Text-Index überhaupt. Das Suffix-Array enthält die Startpositionen aller lexikografisch sortierten Suffixe eines Textes, d.h., wir möchten alle Suffixe eines Textes sortieren. Oft wird das Suffix-Array um das Longest-Common-Prefix-Array (LCP-Array) erweitert. Das LCP-Array enthält die Länge der längsten gemeinsamen Präfixe zweier lexikografisch konsekutiven Suffixe. Abschließend nutzen wir verteilte Suffix- und LCP-Arrays, um den Distributed-Patricia-Trie zu konstruieren. Dieser erlaubt es uns, verschiedene Phrase-Anfragen effizienter zu beantworten, als wenn wir nur das Suffix-Array nutzen.The focus of this dissertation is the parallel construction of text indices. Text indices provide additional information about a text that allow to answer queries faster. Full-text indices for example are used to efficiently answer phrase queries, i.e., if and where a phrase occurs in a text. The research in this dissertation is focused on but not limited to parallel construction algorithms for text indices in both shared and distributed memory. In the first part, we look at wavelet trees: a compact index that generalizes rank and select queries from binary alphabets to alphabets of arbitrary size. In the second part of this dissertation, we consider the suffix array---one of the most researched text indices.The suffix array of a text contains the starting positions of the text's lexicographically sorted suffixes, i.e., we want to sort all its suffixes. Finally, we use the distributed suffix arrays (and LCP arrays) to compute distributed Patricia tries. This allows us to answer different phrase queries more efficiently than using only the suffix array

XBWT Tricks

The eXtended Burrows-Wheeler Transform (XBWT) is a data transformation introduced in [Ferragina et al., FOCS 2005] to com- pactly represent a labeled tree and simultaneously support navigation and path-search operations over its label structure. A natural application of the XBWT is to store a dictionary of strings. A recent extensive experimental study [Martı́nez-Prieto et al., Informa- tion Systems, 2016] shows that, among the available string dictionary implementations, the XBWT is attractive because of its good tradeoff between small space usage, speed, and support for substring searches. In this paper we further investigate the use of the XBWT for storing a string dictionary. Our first contribution is to show how to add suffix links (aka failure links) to a XBWT string dictionary. For a XBWT dictionary with n internal nodes our suffix links can be traversed in constant time and only take 2n + o(n) bits of space. Our second contribution are practical construction algorithms for the XBWT, including the additional data structure supporting the traver- sal of suffix links. Our algorithms build on the many well engineered algorithms for Suffix Array and BWT construction and offer different tradeoffs between running time and working space

Faster Block Tree Construction

The block tree [Belazzougui et al. J. Comput. Syst. Sci. \u2721] is a compressed text index that can answer access (extract a character at a position), rank (number of occurrences of a specified character in a prefix of the text), and select (size of smallest prefix such that a specified character has a specified rank) queries. It requires O(zlog(n/z)) words of space, where z is the number of Lempel-Ziv factors of the text. For some highly repetitive inputs, a block tree can require as little as 0.015 bits per character of the text. Small values of z make the block tree a space-efficient alternative to the wavelet tree, which is another index for these three types of queries. While wavelet trees can be constructed fast in practice, up so far compressed versions of the wavelet tree only leverage statistical compression, meaning that they are blind to spaced repetitions. To make block trees usable in practice, a first step is to find ways in constructing them efficiently. We address this problem by presenting a practically efficient construction algorithm for block trees, which is up to an order of magnitude faster than previous implementations. Additionally, we parallelize our implementation, making it the first block tree construction implementation that works in parallel in shared memory

Compressed Full-Text Indexes for Highly Repetitive Collections

This thesis studies problems related to compressed full-text indexes. A full-text index is a data structure for indexing textual (sequence) data, so that the occurrences of any query string in the data can be found efficiently. While most full-text indexes require much more space than the sequences they index, recent compressed indexes have overcome this limitation. These compressed indexes combine a compressed representation of the index with some extra information that allows decompressing any part of the data efficiently. This way, they provide similar functionality as the uncompressed indexes, while using only slightly more space than the compressed data. The efficiency of data compression is usually measured in terms of entropy. While entropy-based estimates predict the compressed size of most texts accurately, they fail with highly repetitive collections of texts. Examples of such collections include different versions of a document and the genomes of a number of individuals from the same population. While the entropy of a highly repetitive collection is usually similar to that of a text of the same kind, the collection can often be compressed much better than the entropy-based estimate. Most compressed full-text indexes are based on the Burrows-Wheeler transform (BWT). Originally intended for data compression, the BWT has deep connections with full-text indexes such as the suffix tree and the suffix array. With some additional information, these indexes can be simulated with the Burrows-Wheeler transform. The first contribution of this thesis is the first BWT-based index that can compress highly repetitive collections efficiently. Compressed indexes allow us to handle much larger data sets than the corresponding uncompressed indexes. To take full advantage of this, we need algorithms for constructing the compressed index directly, instead of first constructing an uncompressed index and then compressing it. The second contribution of this thesis is an algorithm for merging the BWT-based indexes of two text collections. By using this algorithm, we can derive better space-efficient construction algorithms for BWT-based indexes. The basic BWT-based indexes provide similar functionality as the suffix array. With some additional structures, the functionality can be extended to that of the suffix tree. One of the structures is an array storing the lengths of the longest common prefixes of lexicographically adjacent suffixes of the text. The third contribution of this thesis is a space-efficient algorithm for constructing this array, and a new compressed representation of the array. In the case of individual genomes, the highly repetitive collection can be considered a sample from a larger collection. This collection consists of a reference sequence and a set of possible differences from the reference, so that each sequence contains a subset of the differences. The fourth contribution of this thesis is a BWT-based index that extrapolates the larger collection from the sample and indexes it.Tässä väitöskirjassa käsitellään tiivistettyjä kokotekstihakemistoja tekstimuotoisille aineistoille. Kokotekstihakemistot ovat tietorakenteita, jotka mahdollistavat mielivaltaisten hahmojen esiintymien löytämisen tekstistä tehokkaasti. Perinteiset kokotekstihakemistot, kuten loppuosapuut ja -taulukot, vievät moninkertaisesti tilaa itse aineistoon nähden. Viime aikoina on kuitenkin kehitetty tiivistettyjä hakemistorakenteita, jotka tarjoavat vastaavan toiminnallisuuden alkuperäistä tekstiä pienemmässä tilassa. Tämä on mahdollistanut aikaisempaa suurempien aineistojen käsittelyn. Tekstin tiivistyvyyttä mitataan yleensä suhteessa sen entropiaan. Vaikka entropiaan perustuvat arviot ovat useimmilla aineistoilla varsin tarkkoja, aliarvioivat ne vahvasti toisteisien aineistojen tiivistyvyyttä. Esimerkkejä tällaisista aineistoista ovat kokoelmat saman populaation yksilöiden genomeita tai saman dokumentin eri versioita. Siinä missä tällaisen kokoelman entropia suhteessa aineiston kokoon on vastaava kuin yksittäisellä samaa tyyppiä olevalla tekstillä, tiivistyy kokoelma yleensä huomattavasti paremmin kuin entropian perusteella voisi odottaa. Useimmat tiivistetyt kokotekstihakemistot perustuvat Burrows-Wheeler-muunnokseen (BWT), joka kehitettiin alun perin tekstimuotoisten aineistojen tiivistämiseen. Pian kuitenkin havaittiin, että koska BWT muistuttaa rakenteeltaan loppuosapuuta ja -taulukkoa, voidaan sitä käyttää niissä tehtävien hakujen simulointiin. Tässä väitöskirjassa esitetään ensimmäinen BWT-pohjainen kokotekstihakemisto, joka pystyy tiivistämään vahvasti toisteiset aineistot tehokkaasti. Tiivistettyjen tietorakenteiden käyttö mahdollistaa suurempien aineistoiden käsittelemisen kuin tavallisia tietorakenteita käytettäessä. Tämä etu kuitenkin menetetään, jos tiivistetty tietorakenne muodostetaan luomalla ensin vastaava tavallinen tietorakenne ja tiivistämällä se. Tässä väitöskirjassa esitetään aikaisempaa vähemmän muistia käyttäviä algoritmeja BWT-pohjaisten kokotekstihakemistojen muodostamiseen. Kokoelma yksilöiden genomeita voidaan käsittää otokseksi suuremmasta kokoelmasta, joka koostuu populaation kaikkien yksilöiden sekä niiden hypoteettisten jälkeläisten genomeista. Tällainen kokoelma voidaan esittää äärellisenä automaattina, joka muodostuu referenssigenomista ja yksilöiden genomeissa esiintyvistä poikkeamista referenssistä. Tässä väitöskirjassa esitetään BWT-pohjaisten kokotekstihakemistojen yleistys, joka mahdollistaa tällaisten automaattien indeksoinnin