arXiv subjects

Gregory Kucherov

Publications and source records attributed to Gregory Kucherov.

33 records · Page 2Linked to original sources

arXiv2013

Using cascading Bloom filters to improve the memory usage for de Brujin graphs

De Brujin graphs are widely used in bioinformatics for processing next-generation sequencing data. Due to a very large size of NGS datasets, it is essential to represent de Bruijn graphs compactly, and several approaches to this problem have been proposed recently. In this work, we show how to reduce the memory required by the algorithm of [3] that represents de Brujin graphs using Bloom filters. Our method requires 30% to 40% less memory with respect to the method of [3], with insignificant impact to construction time. At the same time, our experiments showed a better query time compared to [3]. This is, to our knowledge, the best practical representation for de Bruijn graphs.

cs.DS↗

arXiv2012

On-line construction of position heaps

We propose a simple linear-time on-line algorithm for constructing a position heap for a string [Ehrenfeucht et al, 2011]. Our definition of position heap differs slightly from the one proposed in [Ehrenfeucht et al, 2011] in that it considers the suffixes ordered from left to right. Our construction is based on classic suffix pointers and resembles the Ukkonen's algorithm for suffix trees [Ukkonen, 1995]. Using suffix pointers, the position heap can be extended into the augmented position heap that allows for a linear-time string matching algorithm [Ehrenfeucht et al, 2011].

cs.DS↗

arXiv2012

On the combinatorics of suffix arrays

We prove several combinatorial properties of suffix arrays, including a characterization of suffix arrays through a bijection with a certain well-defined class of permutations. Our approach is based on the characterization of Burrows-Wheeler arrays given in [1], that we apply by reducing suffix sorting to cyclic shift sorting through the use of an additional sentinel symbol. We show that the characterization of suffix arrays for a special case of binary alphabet given in [2] easily follows from our characterization. Based on our results, we also provide simple proofs for the enumeration results for suffix arrays, obtained in [3]. Our approach to characterizing suffix arrays is the first that exploits their relationship with Burrows-Wheeler permutations.

cs.DS↗

arXiv2012

Cross-Document Pattern Matching

We study a new variant of the string matching problem called cross-document string matching, which is the problem of indexing a collection of documents to support an efficient search for a pattern in a selected document, where the pattern itself is a substring of another document. Several variants of this problem are considered, and efficient linear-space solutions are proposed with query time bounds that either do not depend at all on the pattern size or depend on it in a very limited way (doubly logarithmic). As a side result, we propose an improved solution to the weighted level ancestor problem.

cs.DS↗

arXiv2011

Linear pattern matching on sparse suffix trees

Packing several characters into one computer word is a simple and natural way to compress the representation of a string and to speed up its processing. Exploiting this idea, we propose an index for a packed string, based on a {\em sparse suffix tree} \cite{KU-96} with appropriately defined suffix links. Assuming, under the standard unit-cost RAM model, that a word can store up to $\log_σn$ characters ($σ$ the alphabet size), our index takes $O(n/\log_σn)$ space, i.e. the same space as the packed string itself. The resulting pattern matching algorithm runs in time $O(m+r^2+r\cdot occ)$, where $m$ is the length of the pattern, $r$ is the actual number of characters stored in a word and $occ$ is the number of pattern occurrences.

cs.DS↗

arXiv2010

Seed design framework for mapping SOLiD reads

The advent of high-throughput sequencing technologies constituted a major advance in genomic studies, offering new prospects in a wide range of applications. We propose a rigorous and flexible algorithmic solution to mapping SOLiD color-space reads to a reference genome. The solution relies on an advanced method of seed design that uses a faithful probabilistic model of read matches and, on the other hand, a novel seeding principle especially adapted to read mapping. Our method can handle both lossy and lossless frameworks and is able to distinguish, at the level of seed design, between SNPs and reading errors. We illustrate our approach by several seed designs and demonstrate their efficiency.

q-bio.QM↗

arXiv2010

Back-translation for discovering distant protein homologies

Frameshift mutations in protein-coding DNA sequences produce a drastic change in the resulting protein sequence, which prevents classic protein alignment methods from revealing the proteins' common origin. Moreover, when a large number of substitutions are additionally involved in the divergence, the homology detection becomes difficult even at the DNA level. To cope with this situation, we propose a novel method to infer distant homology relations of two proteins, that accounts for frameshift and point mutations that may have affected the coding sequences. We design a dynamic programming alignment algorithm over memory-efficient graph representations of the complete set of putative DNA sequences of each protein, with the goal of determining the two putative DNA sequences which have the best scoring alignment under a powerful scoring system designed to reflect the most probable evolutionary process. This allows us to uncover evolutionary information that is not captured by traditional alignment methods, which is confirmed by biologically significant examples.

q-bio.QM↗

arXiv2009

On maximal repetitions of arbitrary exponent

The first two authors have shown [KK99,KK00] that the sum the exponent (and thus the number) of maximal repetitions of exponent at least 2 (also called runs) is linear in the length of the word. The exponent 2 in the definition of a run may seem arbitrary. In this paper, we consider maximal repetitions of exponent strictly greater than 1.

cs.DM↗

arXiv2009

Multiseed Lossless Filtration

We study a method of seed-based lossless filtration for approximate string matching and related bioinformatics applications. The method is based on a simultaneous use of several spaced seeds rather than a single seed as studied by Burkhardt and Kärkkäinen [1]. We present algorithms to compute several important parameters of seed families, study their combinatorial properties, and describe several techniques to construct efficient families. We also report a large-scale application of the proposed technique to the problem of oligonucleotide selection for an EST sequence database.

q-bio.QM↗

arXiv2009

On subset seeds for protein alignment

We apply the concept of subset seeds proposed in [1] to similarity search in protein sequences. The main question studied is the design of efficient seed alphabets to construct seeds with optimal sensitivity/selectivity trade-offs. We propose several different design methods and use them to construct several alphabets. We then perform a comparative analysis of seeds built over those alphabets and compare them with the standard BLASTP seeding method [2], [3], as well as with the family of vector seeds proposed in [4]. While the formalism of subset seeds is less expressive (but less costly to implement) than the cumulative principle used in BLASTP and vector seeds, our seeds show a similar or even better performance than BLASTP on Bernoulli models of proteins compatible with the common BLOSUM62 matrix. Finally, we perform a large-scale benchmarking of our seeds against several main databases of protein alignments. Here again, the results show a comparable or better performance of our seeds vs. BLASTP.

q-bio.QM↗

arXiv2008

Efficient seeding techniques for protein similarity search

We apply the concept of subset seeds proposed in [1] to similarity search in protein sequences. The main question studied is the design of efficient seed alphabets to construct seeds with optimal sensitivity/selectivity trade-offs. We propose several different design methods and use them to construct several alphabets.We then perform an analysis of seeds built over those alphabet and compare them with the standard Blastp seeding method [2,3], as well as with the family of vector seeds proposed in [4]. While the formalism of subset seed is less expressive (but less costly to implement) than the accumulative principle used in Blastp and vector seeds, our seeds show a similar or even better performance than Blastp on Bernoulli models of proteins compatible with the common BLOSUM62 matrix.

q-bio.QM↗

arXiv2006

A unifying framework for seed sensitivity and its application to subset seeds

We propose a general approach to compute the seed sensitivity, that can be applied to different definitions of seeds. It treats separately three components of the seed sensitivity problem -- a set of target alignments, an associated probability distribution, and a seed model -- that are specified by distinct finite automata. The approach is then applied to a new concept of subset seeds for which we propose an efficient automaton construction. Experimental results confirm that sensitive subset seeds can be efficiently designed using our approach, and can then be used in similarity search producing better results than ordinary spaced seeds.

cs.DS↗

arXiv2006

Reconsidering the significance of genomic word frequency

We propose that the distribution of DNA words in genomic sequences can be primarily characterized by a double Pareto-lognormal distribution, which explains lognormal and power-law features found across all known genomes. Such a distribution may be the result of completely random sequence evolution by duplication processes. The parametrization of genomic word frequencies allows for an assessment of significance for frequent or rare sequence motifs.

q-bio.GN↗

arXiv2006

A unifying framework for seed sensitivity and its application to subset seeds (Extended abstract)

We propose a general approach to compute the seed sensitivity, that can be applied to different definitions of seeds. It treats separately three components of the seed sensitivity problem - a set of target alignments, an associated probability distribution, and a seed model - that are specified by distinct finite automata. The approach is then applied to a new concept of subset seeds for which we propose an efficient automaton construction. Experimental results confirm that sensitive subset seeds can be efficiently designed using our approach, and can then be used in similarity search producing better results than ordinary spaced seeds.

cs.OH↗

arXiv2006

Estimating seed sensitivity on homogeneous alignments

We address the problem of estimating the sensitivity of seed-based similarity search algorithms. In contrast to approaches based on Markov models [18, 6, 3, 4, 10], we study the estimation based on homogeneous alignments. We describe an algorithm for counting and random generation of those alignments and an algorithm for exact computation of the sensitivity for a broad class of seed strategies. We provide experimental results demonstrating a bias introduced by ignoring the homogeneousness condition.

cs.OH↗