Lossless filter for multiple repeats with bounded edit distance

Abstract

Background: Identifying local similarity between two or more sequences, or identifying repeats occurring at least twice in a sequence, is an essential part in the analysis of biological sequences and of their phylogenetic relationship. Finding such fragments while allowing for a certain number of insertions, deletions, and substitutions, is however known to be a computationally expensive task, and consequently exact methods can usually not be applied in practice.

Fast algorithms for approximate circular string matching

“…For future work, we will explore the possibility of optimising our algorithms and the corresponding library implementation for the approximate case by using lossless filters for eliminating a possibly large fraction of the input that is guaranteed not to contain any approximate occurrence, such as [ 31 ] for the Hamming distance model or [ 32 ] for the edit distance model. In addition, we will try to improve our algorithms for the approximate case in order to achieve average-case optimality.…”

Motif trie: An efficient text index for pattern discovery with don't cares

“…The literature of algorithmic approaches and software tools for finding motifs and repetitions is vast, as the variability of the problem formulations leads to a variability of algorithmic strategies, and often to combinations of them. For finding long repetitions [39], for example, a preprocessing with an efficient and effective filtering [24,23,28] turns out to be the only possible combinatorial approach. For short motifs there are several enumerative pattern-driven algorithms [19,30,31,34].…”

Circular Sequence Comparison with q-grams

“…An exception to this are the q-gram filtering techniques [32] that have successfully been used for string matching under the edit distance model (e.g. [7,30,26]), as well as for multiple local alignments both under the Hamming [27] and edit [26] distance model.…”

“…We introduce the β-blockwise q-gram distance between two strings x and y, that is, a more powerful generalization of the q-gram distance introduced as a string distance measure in [32]. Intuitively, and similarly to [7,30,26], this generalization comprises partitioning x and y in β blocks each, as evenly as possible, computing the q-gram distance between the corresponding block pairs, and then summing up the distances computed blockwise. 2.…”