arXiv subjects

Solon P. Pissis

Publications and source records attributed to Solon P. Pissis.

64 records · Page 4Linked to original sources

arXiv2016

Optimal Computation of Avoided Words

The deviation of the observed frequency of a word $w$ from its expected frequency in a given sequence $x$ is used to determine whether or not the word is avoided. This concept is particularly useful in DNA linguistic analysis. The value of the standard deviation of $w$, denoted by $std(w)$, effectively characterises the extent of a word by its edge contrast in the context in which it occurs. A word $w$ of length $k>2$ is a $ρ$-avoided word in $x$ if $std(w) \leq ρ$, for a given threshold $ρ< 0$. Notice that such a word may be completely absent from $x$. Hence computing all such words na\"ıvely can be a very time-consuming procedure, in particular for large $k$. In this article, we propose an $O(n)$-time and $O(n)$-space algorithm to compute all $ρ$-avoided words of length $k$ in a given sequence $x$ of length $n$ over a fixed-sized alphabet. We also present a time-optimal $O(σn)$-time and $O(σn)$-space algorithm to compute all $ρ$-avoided words (of any length) in a sequence of length $n$ over an alphabet of size $σ$. Furthermore, we provide a tight asymptotic upper bound for the number of $ρ$-avoided words and the expected length of the longest one. We make available an open-source implementation of our algorithm. Experimental results, using both real and synthetic data, show the efficiency of our implementation.

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arXiv2016

Average-Case Optimal Approximate Circular String Matching

Approximate string matching is the problem of finding all factors of a text t of length n that are at a distance at most k from a pattern x of length m. Approximate circular string matching is the problem of finding all factors of t that are at a distance at most k from x or from any of its rotations. In this article, we present a new algorithm for approximate circular string matching under the edit distance model with optimal average-case search time O(n(k + log m)/m). Optimal average-case search time can also be achieved by the algorithms for multiple approximate string matching (Fredriksson and Navarro, 2004) using x and its rotations as the set of multiple patterns. Here we reduce the preprocessing time and space requirements compared to that approach.

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arXiv2016

Efficient Index for Weighted Sequences

The problem of finding factors of a text string which are identical or similar to a given pattern string is a central problem in computer science. A generalised version of this problem consists in implementing an index over the text to support efficient on-line pattern queries. We study this problem in the case where the text is weighted: for every position of the text and every letter of the alphabet a probability of occurrence of this letter at this position is given. Sequences of this type, also called position weight matrices, are commonly used to represent imprecise or uncertain data. A weighted sequence may represent many different strings, each with probability of occurrence equal to the product of probabilities of its letters at subsequent positions. Given a probability threshold $1/z$, we say that a pattern string $P$ matches a weighted text at position $i$ if the product of probabilities of the letters of $P$ at positions $i,\ldots,i+|P|-1$ in the text is at least $1/z$. In this article, we present an $O(nz)$-time construction of an $O(nz)$-sized index that can answer pattern matching queries in a weighted text in optimal time improving upon the state of the art by a factor of $z \log z$. Other applications of this data structure include an $O(nz)$-time construction of the weighted prefix table and an $O(nz)$-time computation of all covers of a weighted sequence, which improve upon the state of the art by the same factor.

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arXiv2015

Linear-Time Sequence Comparison Using Minimal Absent Words & Applications

Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realized by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free techniques, which are based on measures referring to the composition of sequences in terms of their constituent patterns. These measures, such as $q$-gram distance, are usually computed in time linear with respect to the length of the sequences. In this article, we focus on the complementary idea: how two sequences can be efficiently compared based on information that does not occur in the sequences. A word is an {\em absent word} of some sequence if it does not occur in the sequence. An absent word is {\em minimal} if all its proper factors occur in the sequence. Here we present the first linear-time and linear-space algorithm to compare two sequences by considering {\em all} their minimal absent words. In the process, we present results of combinatorial interest, and also extend the proposed techniques to compare circular sequences.

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arXiv2015

Fast Average-Case Pattern Matching on Weighted Sequences

A weighted string over an alphabet of size $σ$ is a string in which a set of letters may occur at each position with respective occurrence probabilities. Weighted strings, also known as position weight matrices or uncertain sequences, naturally arise in many contexts. In this article, we study the problem of weighted string matching with a special focus on average-case analysis. Given a weighted pattern string $x$ of length $m$, a text string $y$ of length $n>m$, and a cumulative weight threshold $1/z$, defined as the minimal probability of occurrence of factors in a weighted string, we present an algorithm requiring average-case search time $o(n)$ for pattern matching for weight ratio $\frac{z}{m} < \min\{\frac{1}{\log z},\frac{\log σ}{\log z (\log m + \log \log σ)}\}$. For a pattern string $x$ of length $m$, a weighted text string $y$ of length $n>m$, and a cumulative weight threshold $1/z$, we present an algorithm requiring average-case search time $o(σn)$ for the same weight ratio. The importance of these results lies on the fact that these algorithms work in average-case sublinear search time in the size of the text, and in linear preprocessing time and space in the size of the pattern, for these ratios.

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arXiv2015

Linear-Time Superbubble Identification Algorithm for Genome Assembly

DNA sequencing is the process of determining the exact order of the nucleotide bases of an individual's genome in order to catalogue sequence variation and understand its biological implications. Whole-genome sequencing techniques produce masses of data in the form of short sequences known as reads. Assembling these reads into a whole genome constitutes a major algorithmic challenge. Most assembly algorithms utilize de Bruijn graphs constructed from reads for this purpose. A critical step of these algorithms is to detect typical motif structures in the graph caused by sequencing errors and genome repeats, and filter them out; one such complex subgraph class is a so-called superbubble. In this paper, we propose an O(n+m)-time algorithm to detect all superbubbles in a directed acyclic graph with n nodes and m (directed) edges, improving the best-known O(m log m)-time algorithm by Sung et al.

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arXiv2014

Linear-time Computation of Minimal Absent Words Using Suffix Array

An absent word of a word y of length n is a word that does not occur in y. It is a minimal absent word if all its proper factors occur in y. Minimal absent words have been computed in genomes of organisms from all domains of life; their computation provides a fast alternative for measuring approximation in sequence comparison. There exists an O(n)-time and O(n)-space algorithm for computing all minimal absent words on a fixed-sized alphabet based on the construction of suffix automata (Crochemore et al., 1998). No implementation of this algorithm is publicly available. There also exists an O(n^2)-time and O(n)-space algorithm for the same problem based on the construction of suffix arrays (Pinho et al., 2009). An implementation of this algorithm was also provided by the authors and is currently the fastest available. In this article, we bridge this unpleasant gap by presenting an O(n)-time and O(n)-space algorithm for computing all minimal absent words based on the construction of suffix arrays. Experimental results using real and synthetic data show that the respective implementation outperforms the one by Pinho et al.

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arXiv2013

Fast Algorithm for Partial Covers in Words

A factor $u$ of a word $w$ is a cover of $w$ if every position in $w$ lies within some occurrence of $u$ in $w$. A word $w$ covered by $u$ thus generalizes the idea of a repetition, that is, a word composed of exact concatenations of $u$. In this article we introduce a new notion of $α$-partial cover, which can be viewed as a relaxed variant of cover, that is, a factor covering at least $α$ positions in $w$. We develop a data structure of $O(n)$ size (where $n=|w|$) that can be constructed in $O(n\log n)$ time which we apply to compute all shortest $α$-partial covers for a given $α$. We also employ it for an $O(n\log n)$-time algorithm computing a shortest $α$-partial cover for each $α=1,2,\ldots,n$.

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arXiv2013

Order-Preserving Suffix Trees and Their Algorithmic Applications

Recently Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.) introduced order-preserving pattern matching. In this problem we are looking for consecutive substrings of the text that have the same "shape" as a given pattern. These results include a linear-time order-preserving pattern matching algorithm for polynomially-bounded alphabet and an extension of this result to pattern matching with multiple patterns. We make one step forward in the analysis and give an $O(\frac{n\log{n}}{\log\log{n}})$ time randomized algorithm constructing suffix trees in the order-preserving setting. We show a number of applications of order-preserving suffix trees to identify patterns and repetitions in time series.

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arXiv2011

Efficient Seeds Computation Revisited

The notion of the cover is a generalization of a period of a string, and there are linear time algorithms for finding the shortest cover. The seed is a more complicated generalization of periodicity, it is a cover of a superstring of a given string, and the shortest seed problem is of much higher algorithmic difficulty. The problem is not well understood, no linear time algorithm is known. In the paper we give linear time algorithms for some of its versions --- computing shortest left-seed array, longest left-seed array and checking for seeds of a given length. The algorithm for the last problem is used to compute the seed array of a string (i.e., the shortest seeds for all the prefixes of the string) in $O(n^2)$ time. We describe also a simpler alternative algorithm computing efficiently the shortest seeds. As a by-product we obtain an $O(n\log{(n/m)})$ time algorithm checking if the shortest seed has length at least $m$ and finding the corresponding seed. We also correct some important details missing in the previously known shortest-seed algorithm (Iliopoulos et al., 1996).

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