Dynamic Rank/Select Dictionaries with Applications to XML Indexing

We consider a central problem in text indexing: Given a text T over an alphabet C, construct a conlpressed data structure answering the queries char(i), rank,(i); and select,(i) for a synlbol s E C. Wlany data structures consider these queries for static text T [GGVOS; FI\/IOl, SGOG, GMROG]. We consider the dynainic version of the problem, where we are allowed to insert and delete symbols at arbitrary positions of T. This problenl is a key challenge in compressed text illdexing and has direct applicatioil to dynaillic XI\/IL iildexing structures that answer subpath queries [FLMM05]. We build on the results of [RRROZ, GMROG] and give the best known query bounds for the dynanlic version of this problem, supporting arbitrary insertions and deletions of sylllbols in T. Specifically, with an amortized update time of O((l/e)ne), we suggest how to support rank,(i), select,(i): and char(i) queries in O((~/E) loglogn) time, for ally e < 1. The best previous query tinles for this problem were O(logn1og ICI): given by [MNOG]. Our bounds are conlpetitive with state-of-the-art static structures [GhlROG]. Sonle applicable lower bounds for the partial sunls probleln [PD06] show that our update/query tradeoff is also nearly optimal. In addition, our space bound is conlpetitive with the corresponding static structures. For the special case of bitvectors (i.e., 1x1 = 2); we also show the best tradeoffs for query/update time, inlproving upoil the results of [MNOG, HSSO3; RRR021. Finally, our focus on fast query/slower update is well-suited for a query-intensive XhlIL indexing ellvironment. Using the XBW transform [FLhllM05], we also present a dynamic data structure that succinctly maintains an ordered labeled tree T and supports a powerful set of queries on T

Nástroje pro vývoj XB

Predmetom tejto práce sú dva nástroje pre zjednodušenie vývoja kompresného systému XBW. Prvým je knižnica umožnujúca výpis ladiacich informácií, vhodná pre hierarchickú štruktúru modulov XBW. Táto štruktúra je dynamická a môže sa meniť s časom. Druhým je program, kontrolujúci korektnosť fungovania XBW pre jeho rôzne kombinácie parametrov. Parametre pre testovanie sa budú dať zadávať vhodným spôsobom - regulárnymi výrazmi.This thesis discusses two tools for simplifying the development process of XBW compression system. The rst is a library for writing up debug information suitable for the hierarchical structure of XBW modules. Which is a dynamic structure and can change over time. The second is a program which veries correctness of XBW functionality based on selected parameter combinations. Parameter combinations for testing are dened in a suitable manner - with regular expressions.Department of Software EngineeringKatedra softwarového inženýrstvíFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Lossless Text Compression Technique Using Syllable Based Morphology

In this paper, we present a new lossless text compression technique which utilizes syllable-based morphology of multi-syllabic languages. The proposed algorithm is designed to partition words into its syllables and then to produce their shorter bit representations for compression. The method has six main components namely source file, filtering unit, syllable unit, compression unit, dictionary file and target file. The number of bits in coding syllables depends on the number of entries in the dictionary file. The proposed algorithm is implemented and tested using 20 different texts of different lengths collected from different fields. The results indicated a compression of up to 43%

Compressed self-indexed XML representation with efficient XPath evaluation

[Abstract] The popularity of the eXtensible Markup Language (XML) has been continuously growing since its first introduction, being today acknowledged as the de facto standard for semi-structured data representation and data exchange on the World Wide Web. In this scenario, several query languages were proposed to exploit the expressiveness of XML data, as well as systems to provide an eficient support. At the same time, as research in compression became more and more relevant, works also focused their efforts on studying new approaches to provide eficient solutions, using the minimum amount of space. Today, however, there is a lack of practical available tools that join both eficient query support, and minimum space requirements. In this thesis we address this problem, and propose a new approach for storing, processing and querying XML documents in time and space eficient way, by specially focusing on XPath queries. We have developed a new compressed selfindexed representation of XML documents that obtains compression ratios about 30%-40%, over which a query module providing eficient XPath query evaluation has also been developed. As a whole, both parts make up a complete system, we called XXS, for the eficient evaluation of XPath queries over compressed self-indexed XML documents. Experimental results show the outstanding performance of our proposal, which can successfully compete with some of the best-known solutions, and that largely outperforms them in terms of space.[Resumo] A popularidade do eXtensible Markup Language (XML) non fixo máis que medrar dende a súa introdución inicial, sendo recoñecido hoxe en día como o estándar de facto para a representación de datos semi-estruturados e o intercambio de datos na Rede. Baixo este escenario, son varias as linguaxes de consulta que se propuxeron para explotar a expresividade dos datos en formato XML, así como sistemas que proporcionasen un soporte eficiente a eles. Ó mesmo tempo, e conforme a investigación en compresión se fixo cada vez máis relevante, os esforzos tamén foron dirixidos a estudiar novas aproximacións que ofrecesen solucións eficientes, pero usando ademáis a menor cantidade de espacio posible. Actualmente, sen embargo, existe unha clara ausencia de ferramentas prácticas dispoñibles que agrupen ambas características: un soporte á realización de consultas eficiente, xunto con requisitos de espacio mínimos. Nesta tese abordamos ese problema, e propoñemos unha nova solución para o almacenamento, procesamento e consulta de documentos XML, eficiente tanto en tempo como en espacio, centrándonos, en particular, na linguaxe de consulta XPath. Así, desenvolvimos unha nova representación comprimida e auto-indexada de documentos XML, que obtén ratios de compresión en torno ó 30%-40%, e sobre a cal se creou tamén un módulo de consulta para a eficiente evaluación de consultas XPath. En conxunto, ambas contribucións conforman un sistema completo, que chamamos XXS, para a evaluación eficiente de consultas XPath sobre documentos XML comprimidos e auto-indexados. Os resultados experimentais amosan o destacado comportamento da nosa ferramenta, que é capaz de competir exitosamente con algunhas das solucións máis coñecidas, ás que ademáis supera claramente en termos de espacio.[Resumen] La popularidad del eXtensible Markup Language (XML) no ha hecho sino más que ir en aumento desde su introducción inicial, siendo hoy día reconocido como el estándar de facto para la representación de datos semi-estructurados, y el intercambio de datos en Internet. Bajo este escenario, son varios los lenguajes de consulta que se han venido proponiendo para explotar la expresividad de los datos en formato XML, así como sistemas que proporcionasen un soporte eficiente a ellos. Al mismo tiempo, y conforme la investigación en compresión se ha hecho cada vez más relevante, los esfuerzos se han dirigido también a estudiar nuevas aproximaciones que ofreciesen soluciones eficientes, pero usando además la menor cantidad de espacio posible. Actualmente, sin embargo, existe una clara ausencia de herramientas prácticas disponibles que aúnen ambas características: un soporte a la realización de consultas eficiente, con requisitos de espacio mínimos. En esta tesis abordamos ese problema, y proponemos una nueva solución para el almacenamiento, procesamiento y consulta de documentos XML, eficiente en tiempo y en espacio, centrándonos, en particular, en el lenguaje de consulta XPath. Así, hemos desarrollado una nueva representación comprimida y auto-indexada de documentos XML, que obtiene ratios de compresión del 30%-40%, y sobre la cual se ha creado un módulo de consulta para la eficiente evaluación de consultas XPath. En conjunto, ambas contribuciones conforman un sistema completo, que hemos dado en llamar XXS, para la evaluación eficiente de consultas XPath sobre documentos XML comprimidos y auto-indexados. Los resultados experimentales evidencian el destacado comportamiento de nuestra herramienta, que es capaz de competir exitosamente con algunas de las soluciones más conocidas, a las que además supera claramente en términos de espacio

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

SIQXC: Schema Independent Queryable XML Compression for Smartphones

The explosive growth of XML use over the last decade has led to a lot of research on how to best store and access it. This growth has resulted in XML being described as a de facto standard for storage and exchange of data over the web. However, XML has high redundancy because of its self-­‐ describing nature making it verbose. The verbose nature of XML poses a storage problem. This has led to much research devoted to XML compression. It has become of more interest since the use of resource constrained devices is also on the rise. These devices are limited in storage space, processing power and also have finite energy. Therefore, these devices cannot cope with storing and processing large XML documents. XML queryable compression methods could be a solution but none of them has a query processor that runs on such devices. Currently, wireless connections are used to alleviate the problem but they have adverse effects on the battery life. They are therefore not a sustainable solution. This thesis describes an attempt to address this problem by proposing a queryable compressor (SIQXC) with a query processor that runs in a resource constrained environment thereby lowering wireless connection dependency yet alleviating the storage problem. It applies a novel simple 2 tuple integer encoding system, clustering and gzip. SIQXC achieves an average compression ratio of 70% which is higher than most queryable XML compressors and also supports a wide range of XPATH operators making it competitive approach. It was tested through a practical implementation evaluated against the real data that is usually used for XML benchmarking. The evaluation covered the compression ratio, compression time and query evaluation accuracy and response time. SIQXC allows users to some extent locally store and manipulate the otherwise verbose XML on their Smartphones

Processing and indexing large biological datasets using the Burrows-Wheeler Transform of string collections

In the last few decades, the advent of next-generation sequencing technologies (NGS) has dramatically reduced the cost of DNA sequencing. This has made it possible to sequence many genomes in very little time, paving the way for projects which aim at the creation of large and repetitive collections of genomic sequences. The abundance of biological data is driving the development of new memory-efficient algorithms and data structures that can scale for large datasets, thus tackling the high computational burden related to processing these data. This trend has a strong impact on the text algorithms area. In this thesis, we will study the Burrows-Wheeler Transform for processing, indexing, and compressing collections of strings. Data compression addresses the problem of encoding the input to reduce the space needed for storing it, while text indexing focuses on finding ways to efficiently process and extract information from the data. In bioinformatics, these two concepts have been frequently used together since they allow the design of data structures that can efficiently process biological data while keeping the input compressed. The Burrows-Wheeler Transform (BWT) is a reversible transformation on strings introduced by Michael Burrows and David J. Wheeler in 1994 that plays a central role in this area. It is the key component of several compressed data structures for text processing, like the FM-index [Ferraggina and Manzini, SODA, 2000] or the r-index [Gagie et al., SODA, 2018], and some of the most important software in bioinformatics, such as the well-known Bowtie [Langmead et al., Genome Biology, 2009] and BWA [Li and Durbin, Bioinformatics, 2010]. The BWT was originally defined for individual strings, so when the focus moved from single sequences to string collections, there was the need to extend this transform. Over the years, several different tools and algorithms for computing BWT of string collections were introduced. However, even if the transforms generated by these tools frequently differ from each other, the problem of characterizing the BWT variants was never addressed properly. In this thesis, we close this gap by presenting the first systematic study of the BWT of string collections. We identified five non-equivalent variants computed by the tools in current use and analyzed their properties to show how exactly they differ. We complete our theoretical analysis by comparing the five BWT variants on several real-life biological datasets. We show that not only the differences among the resulting transforms can be extensive, but they also lead to significant changes in the compressibility of the BWT of the underlying string collection. As a further complication, the BWT variants in use often depend on the input order of the sequences. This significantly impacts the number of runs r, which defines the size of BWT-based compressed data structures. In this thesis, we address the problem of reordering the input sequences by providing the first implementation of the algorithm of Bentley et al. [ESA 2020], which computes the order minimizing the number of runs of the BWT. This leads to the creation of the first tool for computing the optimal BWT, i.e., the BWT variant which guarantees the minimum number of runs. We show experimentally that the input order can dramatically affect the final result: on our real-life datasets, the optimal BWT had up to 31 times fewer runs than the BWT computed without reordering the input sequences. The extended BWT (eBWT) of Mantaci et al. [Theor. Comput. Sci. 2007] is one of the first BWT variants explicitly designed to process string collections. Even though this transform is mathematically sound and has useful properties, its construction has been a problem for more than a decade. In this thesis, we present two linear-time algorithms for computing the eBWT of large string collections. The first is an improvement of the Bijective BWT construction algorithm of Bannai et al. [CPM 2019], while the second uses the Prefix-free parsing (PFP) method [Boucher et al., Algorithms Mol. Biol., 2019] to specifically process large and repetitive genomic sequence collections. In the final part of the thesis, we conclude by studying, for the first time, how to index string collections using the eBWT. We present the extended r-index, an extension of the r-index to the eBWT, which maintains the same performance as the original r-index while inheriting the properties of the eBWT. We implemented this data structure using a variant of the PFP algorithm and tested it on real-life biological datasets containing circular bacterial genomes and plasmids. We show experimentally that our index has competitive query times compared to the r-index on different pattern lengths while supporting advanced pattern matching functionalities on circular sequences

Scalable succinct indexing for large text collections

Self-indexes save space by emulating operations of traditional data structures using basic operations on bitvectors. Succinct text indexes provide full-text search functionality which is traditionally provided by suffix trees and suffix arrays for a given text, while using space equivalent to the compressed representation of the text. Succinct text indexes can therefore provide full-text search functionality over inputs much larger than what is viable using traditional uncompressed suffix-based data structures. Fields such as Information Retrieval involve the processing of massive text collections. However, the in-memory space requirements of succinct text indexes during construction have hampered their adoption for large text collections. One promising approach to support larger data sets is to avoid constructing the full suffix array by using alternative indexing representations. This thesis focuses on several aspects related to the scalability of text indexes to larger data sets. We identify practical improvements in the core building blocks of all succinct text indexing algorithms, and subsequently improve the index performance on large data sets. We evaluate our findings using several standard text collections and demonstrate: (1) the practical applications of our improved indexing techniques; and (2) that succinct text indexes are a practical alternative to inverted indexes for a variety of top-k ranked document retrieval problems

Graphical pangenomics

Completely sequencing genomes is expensive, and to save costs we often analyze new genomic data in the context of a reference genome. This approach distorts our image of the inferred genome, an effect which we describe as reference bias. To mitigate reference bias, I repurpose graphical models previously used in genome assembly and alignment to serve as a reference system in resequencing. To do so I formalize the concept of a variation graph to link genomes to a graphical model of their mutual alignment that is capable of representing any kind of genomic variation, both small and large. As this model combines both sequence and variation information in one structure it serves as a natural basis for resequencing. By indexing the topology, sequence space, and haplotype space of these graphs and developing generalizations of sequence alignment suitable to them, I am able to use them as reference systems in the analysis of a wide array of genomic systems, from large vertebrate genomes to microbial pangenomes. To demonstrate the utility of this approach, I use my implementation to solve resequencing and alignment problems in the context of Homo sapiens and Saccharomyces cerevisiae. I use graph visualization techniques to explore variation graphs built from a variety of sources, including diverged human haplotypes, a gut microbiome, and a freshwater viral metagenome. I find that variation aware read alignment can eliminate reference bias at known variants, and this is of particular importance in the analysis of ancient DNA, where existing approaches result in significant bias towards the reference genome and concomitant distortion of population genetics results. I validate that the variation graph model can be applied to align RNA sequencing data to a splicing graph. Finally, I show that a classical pangenomic inference problem in microbiology can be solved using a resequencing approach based on variation graphs.Wellcome Trust PhD fellowshi