Compact q-gram Profiling of Compressed Strings

We consider the problem of computing the q-gram profile of a string \str of size $N$ compressed by a context-free grammar with $n$ production rules. We present an algorithm that runs in $O(N-\alpha)$ expected time and uses O(n+q+\kq) space, where $N-\alpha\leq qn$ is the exact number of characters decompressed by the algorithm and \kq\leq N-\alpha is the number of distinct q-grams in \str. This simultaneously matches the current best known time bound and improves the best known space bound. Our space bound is asymptotically optimal in the sense that any algorithm storing the grammar and the q-gram profile must use \Omega(n+q+\kq) space. To achieve this we introduce the q-gram graph that space-efficiently captures the structure of a string with respect to its q-grams, and show how to construct it from a grammar

Rank, select and access in grammar-compressed strings

Given a string $S$ of length $N$ on a fixed alphabet of $\sigma$ symbols, a grammar compressor produces a context-free grammar $G$ of size $n$ that generates $S$ and only $S$. In this paper we describe data structures to support the following operations on a grammar-compressed string: \mbox{rank}_c(S,i) (return the number of occurrences of symbol $c$ before position $i$ in $S$); \mbox{select}_c(S,i) (return the position of the $i$th occurrence of $c$ in $S$); and \mbox{access}(S,i,j) (return substring $S[i,j]$). For rank and select we describe data structures of size $O(n\sigma\log N)$ bits that support the two operations in $O(\log N)$ time. We propose another structure that uses $O(n\sigma\log (N/n)(\log N)^{1+\epsilon})$ bits and that supports the two queries in $O(\log N/\log\log N)$, where $\epsilon>0$ is an arbitrary constant. To our knowledge, we are the first to study the asymptotic complexity of rank and select in the grammar-compressed setting, and we provide a hardness result showing that significantly improving the bounds we achieve would imply a major breakthrough on a hard graph-theoretical problem. Our main result for access is a method that requires $O(n\log N)$ bits of space and $O(\log N+m/\log_\sigma N)$ time to extract $m=j-i+1$ consecutive symbols from $S$. Alternatively, we can achieve $O(\log N/\log\log N+m/\log_\sigma N)$ query time using $O(n\log (N/n)(\log N)^{1+\epsilon})$ bits of space. This matches a lower bound stated by Verbin and Yu for strings where $N$ is polynomially related to $n$.Comment: 16 page

Fast and Tiny Structural Self-Indexes for XML

XML document markup is highly repetitive and therefore well compressible using dictionary-based methods such as DAGs or grammars. In the context of selectivity estimation, grammar-compressed trees were used before as synopsis for structural XPath queries. Here a fully-fledged index over such grammars is presented. The index allows to execute arbitrary tree algorithms with a slow-down that is comparable to the space improvement. More interestingly, certain algorithms execute much faster over the index (because no decompression occurs). E.g., for structural XPath count queries, evaluating over the index is faster than previous XPath implementations, often by two orders of magnitude. The index also allows to serialize XML results (including texts) faster than previous systems, by a factor of ca. 2-3. This is due to efficient copy handling of grammar repetitions, and because materialization is totally avoided. In order to compare with twig join implementations, we implemented a materializer which writes out pre-order numbers of result nodes, and show its competitiveness.Comment: 13 page

Efficient Storage of Genomic Sequences in High Performance Computing Systems

ABSTRACT: In this dissertation, we address the challenges of genomic data storage in high performance computing systems. In particular, we focus on developing a referential compression approach for Next Generation Sequence data stored in FASTQ format files. The amount of genomic data available for researchers to process has increased exponentially, bringing enormous challenges for its efficient storage and transmission. General-purpose compressors can only offer limited performance for genomic data, thus the need for specialized compression solutions. Two trends have emerged as alternatives to harness the particular properties of genomic data: non-referential and referential compression. Non-referential compressors offer higher compression rations than general purpose compressors, but still below of what a referential compressor could theoretically achieve. However, the effectiveness of referential compression depends on selecting a good reference and on having enough computing resources available. This thesis presents one of the first referential compressors for FASTQ files. We first present a comprehensive analytical and experimental evaluation of the most relevant tools for genomic raw data compression, which led us to identify the main needs and opportunities in this field. As a consequence, we propose a novel compression workflow that aims at improving the usability of referential compressors. Subsequently, we discuss the implementation and performance evaluation for the core of the proposed workflow: a referential compressor for reads in FASTQ format that combines local read-to-reference alignments with a specialized binary-encoding strategy. The compression algorithm, named UdeACompress, achieved very competitive compression ratios when compared to the best compressors in the current state of the art, while showing reasonable execution times and memory use. In particular, UdeACompress outperformed all competitors when compressing long reads, typical of the newest sequencing technologies. Finally, we study the main aspects of the data-level parallelism in the Intel AVX-512 architecture, in order to develop a parallel version of the UdeACompress algorithms to reduce the runtime. Through the use of SIMD programming, we managed to significantly accelerate the main bottleneck found in UdeACompress, the Suffix Array Construction

Drawing Elena Ferrante's Profile. Workshop Proceedings, Padova, 7 September 2017

Elena Ferrante is an internationally acclaimed Italian novelist whose real identity has been kept secret by E/O publishing house for more than 25 years. Owing to her popularity, major Italian and foreign newspapers have long tried to discover her real identity. However, only a few attempts have been made to foster a scientific debate on her work. In 2016, Arjuna Tuzzi and Michele Cortelazzo led an Italian research team that conducted a preliminary study and collected a well-founded, large corpus of Italian novels comprising 150 works published in the last 30 years by 40 different authors. Moreover, they shared their data with a select group of international experts on authorship attribution, profiling, and analysis of textual data: Maciej Eder and Jan Rybicki (Poland), Patrick Juola (United States), Vittorio Loreto and his research team, Margherita Lalli and Francesca Tria (Italy), George Mikros (Greece), Pierre Ratinaud (France), and Jacques Savoy (Switzerland). The chapters of this volume report the results of this endeavour that were first presented during the international workshop Drawing Elena Ferrante's Profile in Padua on 7 September 2017 as part of the 3rd IQLA-GIAT Summer School in Quantitative Analysis of Textual Data. The fascinating research findings suggest that Elena Ferrante\u2019s work definitely deserves \u201cmany hands\u201d as well as an extensive effort to understand her distinct writing style and the reasons for her worldwide success

Novel computational techniques for mapping and classifying Next-Generation Sequencing data

Since their emergence around 2006, Next-Generation Sequencing technologies have been revolutionizing biological and medical research. Quickly obtaining an extensive amount of short or long reads of DNA sequence from almost any biological sample enables detecting genomic variants, revealing the composition of species in a metagenome, deciphering cancer biology, decoding the evolution of living or extinct species, or understanding human migration patterns and human history in general. The pace at which the throughput of sequencing technologies is increasing surpasses the growth of storage and computer capacities, which creates new computational challenges in NGS data processing. In this thesis, we present novel computational techniques for read mapping and taxonomic classification. With more than a hundred of published mappers, read mapping might be considered fully solved. However, the vast majority of mappers follow the same paradigm and only little attention has been paid to non-standard mapping approaches. Here, we propound the so-called dynamic mapping that we show to significantly improve the resulting alignments compared to traditional mapping approaches. Dynamic mapping is based on exploiting the information from previously computed alignments, helping to improve the mapping of subsequent reads. We provide the first comprehensive overview of this method and demonstrate its qualities using Dynamic Mapping Simulator, a pipeline that compares various dynamic mapping scenarios to static mapping and iterative referencing. An important component of a dynamic mapper is an online consensus caller, i.e., a program collecting alignment statistics and guiding updates of the reference in the online fashion. We provide Ococo, the first online consensus caller that implements a smart statistics for individual genomic positions using compact bit counters. Beyond its application to dynamic mapping, Ococo can be employed as an online SNP caller in various analysis pipelines, enabling SNP calling from a stream without saving the alignments on disk. Metagenomic classification of NGS reads is another major topic studied in the thesis. Having a database with thousands of reference genomes placed on a taxonomic tree, the task is to rapidly assign a huge amount of NGS reads to tree nodes, and possibly estimate the relative abundance of involved species. In this thesis, we propose improved computational techniques for this task. In a series of experiments, we show that spaced seeds consistently improve the classification accuracy. We provide Seed-Kraken, a spaced seed extension of Kraken, the most popular classifier at present. Furthermore, we suggest ProPhyle, a new indexing strategy based on a BWT-index, obtaining a much smaller and more informative index compared to Kraken. We provide a modified version of BWA that improves the BWT-index for a quick k-mer look-up