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

Sampled longest common prefix array

When augmented with the longest common prefix (LCP) array and some other structures, the suffix array can solve many string processing problems in optimal time and space. A compressed representation of the LCP array is also one of the main building blocks in many compressed suffix tree proposals. In this paper, we describe a new compressed LCP representation: the sampled LCP array. We show that when used with a compressed suffix array (CSA), the sampled LCP array often offers better time/space trade-offs than the existing alternatives. We also show how to construct the compressed representations of the LCP array directly from a CS

Relative Select

Motivated by the problem of storing coloured de Bruijn graphs, we show how, if we can already support fast select queries on one string, then we can store a little extra information and support fairly fast select queries on a similar string

Distribution-Aware Compressed Full-Text Indexes

Peer reviewe

Indexing Finite Language Representation of Population Genotypes

With the recent advances in DNA sequencing, it is now possible to have complete genomes of individuals sequenced and assembled. This rich and focused genotype information can be used to do different population-wide studies, now first time directly on whole genome level. We propose a way to index population genotype information together with the complete genome sequence, so that one can use the index to efficiently align a given sequence to the genome with all plausible genotype recombinations taken into account. This is achieved through converting a multiple alignment of individual genomes into a finite automaton recognizing all strings that can be read from the alignment by switching the sequence at any time. The finite automaton is indexed with an extension of Burrows-Wheeler transform to allow pattern search inside the plausible recombinant sequences. The size of the index stays limited, because of the high similarity of individual genomes. The index finds applications in variation calling and in primer design. On a variation calling experiment, we found about 1.0% of matches to novel recombinants just with exact matching, and up to 2.4% with approximate matching.Comment: This is the full version of the paper that was presented at WABI 2011. The implementation is available at http://www.cs.helsinki.fi/group/suds/gcsa

Storage and Retrieval of Highly Repetitive Sequence Collections

Peer reviewe

Storage and Retrieval of Individual Genomes and other Repetitive Sequence Collections

Computing Reviews (1998) Categories and Subject Descriptors: E.4 Coding and Information Theory — data compaction and compression F.2.2 Analysis of Algorithms and Problem Complexity: Nonnumerical Algorithms and Problems — pattern matching, sorting and searchingIn the near future, biomolecular engineering techniques will reach a state where the sequencing of individual genomes becomes feasible. This progress will create huge expectations for the data analysis domain to reveal new knowledge on the ”secrets of life”. Quite rudimentary reasons may inhibit such breakthroughs; it may not be feasible to store all the data in a form that would enable anything but most basic data analysis routines to be executed. This paper is devoted into studying ways to store massive sets of complete individual genomes in space-efficient manner so that retrieval of the content as well as queries on the content of the sequences can be provided time-efficiently. We show that although the state-of-the-art full-text self-indexes do not yet provide satisfactory space bounds for this specific task, after carefully engineering those structures it is possible to achieve very attractive results; the new structures are fully able to exploit the fact that the individual genomes are highly similar. We confirm the theoretical findings by experiments on large DNA sequences, and also on version control data, that forms another application domain for our methods

Haplotype-aware graph indexes.

MOTIVATION: The variation graph toolkit (VG) represents genetic variation as a graph. Although each path in the graph is a potential haplotype, most paths are non-biological, unlikely recombinations of true haplotypes. RESULTS: We augment the VG model with haplotype information to identify which paths are more likely to exist in nature. For this purpose, we develop a scalable implementation of the graph extension of the positional Burrows-Wheeler transform. We demonstrate the scalability of the new implementation by building a whole-genome index of the 5008 haplotypes of the 1000 Genomes Project, and an index of all 108 070 Trans-Omics for Precision Medicine Freeze 5 chromosome 17 haplotypes. We also develop an algorithm for simplifying variation graphs for k-mer indexing without losing any k-mers in the haplotypes. AVAILABILITY AND IMPLEMENTATION: Our software is available at https://github.com/vgteam/vg, https://github.com/jltsiren/gbwt and https://github.com/jltsiren/gcsa2. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online