Universal Indexes for Highly Repetitive Document Collections

Indexing highly repetitive collections has become a relevant problem with the emergence of large repositories of versioned documents, among other applications. These collections may reach huge sizes, but are formed mostly of documents that are near-copies of others. Traditional techniques for indexing these collections fail to properly exploit their regularities in order to reduce space. We introduce new techniques for compressing inverted indexes that exploit this near-copy regularity. They are based on run-length, Lempel-Ziv, or grammar compression of the differential inverted lists, instead of the usual practice of gap-encoding them. We show that, in this highly repetitive setting, our compression methods significantly reduce the space obtained with classical techniques, at the price of moderate slowdowns. Moreover, our best methods are universal, that is, they do not need to know the versioning structure of the collection, nor that a clear versioning structure even exists. We also introduce compressed self-indexes in the comparison. These are designed for general strings (not only natural language texts) and represent the text collection plus the index structure (not an inverted index) in integrated form. We show that these techniques can compress much further, using a small fraction of the space required by our new inverted indexes. Yet, they are orders of magnitude slower.Comment: This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie Actions H2020-MSCA-RISE-2015 BIRDS GA No. 69094

Indexing large genome collections on a PC

Motivation: The availability of thousands of invidual genomes of one species should boost rapid progress in personalized medicine or understanding of the interaction between genotype and phenotype, to name a few applications. A key operation useful in such analyses is aligning sequencing reads against a collection of genomes, which is costly with the use of existing algorithms due to their large memory requirements. Results: We present MuGI, Multiple Genome Index, which reports all occurrences of a given pattern, in exact and approximate matching model, against a collection of thousand(s) genomes. Its unique feature is the small index size fitting in a standard computer with 16--32\,GB, or even 8\,GB, of RAM, for the 1000GP collection of 1092 diploid human genomes. The solution is also fast. For example, the exact matching queries are handled in average time of 39\,$\mu$s and with up to 3 mismatches in 373\,$\mu$s on the test PC with the index size of 13.4\,GB. For a smaller index, occupying 7.4\,GB in memory, the respective times grow to 76\,$\mu$s and 917\,$\mu$s. Availability: Software and Suuplementary material: \url{http://sun.aei.polsl.pl/mugi}

siEDM: an efficient string index and search algorithm for edit distance with moves

Although several self-indexes for highly repetitive text collections exist, developing an index and search algorithm with editing operations remains a challenge. Edit distance with moves (EDM) is a string-to-string distance measure that includes substring moves in addition to ordinal editing operations to turn one string into another. Although the problem of computing EDM is intractable, it has a wide range of potential applications, especially in approximate string retrieval. Despite the importance of computing EDM, there has been no efficient method for indexing and searching large text collections based on the EDM measure. We propose the first algorithm, named string index for edit distance with moves (siEDM), for indexing and searching strings with EDM. The siEDM algorithm builds an index structure by leveraging the idea behind the edit sensitive parsing (ESP), an efficient algorithm enabling approximately computing EDM with guarantees of upper and lower bounds for the exact EDM. siEDM efficiently prunes the space for searching query strings by the proposed method, which enables fast query searches with the same guarantee as ESP. We experimentally tested the ability of siEDM to index and search strings on benchmark datasets, and we showed siEDM's efficiency.Comment: 23 page

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

Database indexing for production MegaBLAST searches

Motivation: The BLAST software package for sequence comparison speeds up homology search by preprocessing a query sequence into a lookup table. Numerous research studies have suggested that preprocessing the database instead would give better performance. However, production usage of sequence comparison methods that preprocess the database has been limited to programs such as BLAT and SSAHA that are designed to find matches when query and database subsequences are highly similar

Data compression for sequencing data

Post-Sanger sequencing methods produce tons of data, and there is a general agreement that the challenge to store and process them must be addressed with data compression. In this review we first answer the question “why compression” in a quantitative manner. Then we also answer the questions “what” and “how”, by sketching the fundamental compression ideas, describing the main sequencing data types and formats, and comparing the specialized compression algorithms and tools. Finally, we go back to the question “why compression” and give other, perhaps surprising answers, demonstrating the pervasiveness of data compression techniques in computational biology