Efficient Pattern Matching in Elastic-Degenerate Texts

Abstract

In this paper, we extend the notion of gapped strings to elastic-degenerate strings. An elastic-degenerate string can been seen as an ordered collection of k > 1 seeds (substrings/subpatterns) interleaved by elastic-degenerate symbols such that each elastic-degenerate symbol corresponds to a set of two or more variable length strings. Here, we present an algorithm for solving the pattern matching problem with (solid) pattern and elastic-degenerate text, running in O(N +αγnm) time; where m is the length of the given pattern; n and N are the length and total size of the given elastic-degenerate text, respectively; α and γ are small constants, respectively representing the maximum number of strings in any elastic-degenerate symbol of the text and the largest number of elastic-degenerate symbols spanned by any occurrence of the pattern in the text. The space used by the algorithm is linear in the size of the input for a constant number of elastic-degenerate symbols in the text; α and γ are so small in real applications that the algorithm is expected to work very efficiently in practice.

Approximate pattern matching on elastic-degenerate text

“…Since genomic sequences are endowed with polymorphisms and sequencing errors, the existence of an exact occurrence can result into a strong assumption. The aim of this work is to generalize the studies of [11] and [27] for the exact case, allowing some approximation in the occurrences of the input pattern. We suggest a simple on-line O(kmG + kN)-time and O(m)-space algorithm, G being the total number of strings in T and k > 0 the maximum number of allowed substitutions in a pattern's occurrence, that is nonzero Hamming distance.…”

“…In the literature, many different (compressed) representations and thus algorithms have been considered for pattern matching on a set of similar texts [4][5][6][7][8][9][10]. A natural representation of pan-genomes, or fragments of them, that we consider here are elastic-degenerate texts [11]. An elastic-degenerate text is a sequence which compactly represents a multiple alignment of several closely-related sequences.…”

“…A few results exist on the (exact) EDSM problem. In [11], an algorithm for solving the EDSM problem in time O(αγ mn + N) and space O(N) was presented, where α and γ are parameters, respectively representing the maximum number of strings in any degenerate segment of the text and the maximum number of degenerate segments spanned by any occurrence of the pattern in the text. In [27], two new algorithms to solve the same problem in an on-line manner 1 , where w is the size of the computer word in the word-RAM model.…”

Why High-Performance Modelling and Simulation for Big Data Applications Matters

“…We present here a natural representation of pan-genomes (whole genomes or their fragments): elastic-degenerate texts. An elastic-degenerate text (ED-text) is a sequence compactly representing a multiple alignment of several closely-related sequences: substrings that match exactly are collapsed, while those in positions where the sequences differ (by means of substitutions, insertions, and deletions of substrings) are called degenerate, and therein all possible variants observed at that location are listed [105]. Actually, ED-texts correspond exactly to the Variant Call Format (.vcf), the standard for files storing genomic variations [106].…”

Pattern Matching on Elastic-Degenerate Text with Errors

“…In the literature, many different (compressed) representations and thus algorithms have been considered for pattern matching on a set of similar texts [4,5,16,21,6,3,12]. A natural representation of pan-genomes, or fragments of them, that we consider here are elastic-degenerate texts [11]. An elastic-degenerate text is a sequence which compactly represents a multiple alignment of several closely-related sequences.…”