Longest common substrings with k mismatches

Flouri, Tomáš; Giaquinta, Emanuele; Kobert, Kassian; Ukkonen, Esko

doi:10.1016/j.ipl.2015.03.006

Cited by 33 publications

(31 citation statements)

References 11 publications

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“…The longest common substring with one mismatch problem was first considered in [6], where an O(n 2 )-time and O(n)-space solution was given. This result was further improved by Flouri et al [14], who showed an O(n log n)-time and O(n)-space solution.…”

Section: Related Workmentioning

confidence: 80%

Longest Common Substring with Approximately k Mismatches

2019

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In the longest common substring problem, we are given two strings of length n and must find a substring of maximal length that occurs in both strings. It is well known that the problem can be solved in linear time, but the solution is not robust and can vary greatly when the input strings are changed even by one character. To circumvent this, Leimeister and Morgenstern introduced the problem of the longest common substring with k mismatches. Lately, this problem has received a lot of attention in the literature. In this paper, we first show a conditional lower bound based on the SETH hypothesis implying that there is little hope to improve existing solutions. We then introduce a new but closely related problem of the longest common substring with approximately k mismatches and use locality-sensitive hashing to show that it admits a solution with strongly subquadratic running time. We also apply these results to obtain a strongly subquadratic-time 2-approximation algorithm for the longest common substring with k mismatches problem and show conditional hardness of improving its approximation ratio. * This is a full and extended version of the conference paper [31].

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Section: Related Workmentioning

confidence: 80%

Longest Common Substring with Approximately k Mismatches

2019

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“…suffix tree of sequences in reverse to find the longest repeats with k consecutive mismatches among two strings. A modified version of Crochemore’s algorithm was developed by Flouri et al Flouri et al (2015) for finding longest common substring with one mismatch. The above method could be extended for more than two sequences, as employed in STAG-CNS, by using a generalized suffix tree and a reverse generalized suffix tree.…”

Section: Discussionmentioning

confidence: 99%

STAG-CNS: An Order-Aware Conserved Non-coding Sequences Discovery Tool For Arbitrary Numbers of Species

Lai

Behera

Liang

et al. 2017

Preprint

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One method for identifying noncoding regulatory regions of a genome is to quantify rates of divergence between related species, as functional sequence will generally diverge more slowly. Most approaches to identifying these conserved noncoding sequences (CNS) based on alignment have had relatively large minimum sequence lengths ( 15 base pair) compared to the average length of known transcription factor binding sites. To circumvent this constraint, STAG-CNS integrates data from the promoters of conserved orthologous genes in three or more species simultaneously. Using data from up to six grass species made it possible to identify conserved sequences as short at 9 base pairs with FDP 0.05. These CNS exhibit greater overlap with open chromatin regions identified using DNase I hypersensitivity, and are enriched in the promoters of genes involved in transcriptional regulation. STAG-CNS was further employed to characterize loss of conserved noncoding sequences associated with retained duplicate genes from the ancient maize polyploidy. Genes with fewer retained CNS show lower overall expression, although this bias is more apparent in samples of complex organ systems containing many cell types, suggesting CNS loss may correspond to a reduced number of expression contexts rather than lower expression levels across the entire ancestral expression domain.

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“…Alignment problems have sustained interest in the computer science community over many decades (see e.g., book [4]). The edit metric has been recently well-studied in the streaming model, e.g., [3], [5], [9], [10], [6]), and "mismatches" in the Hamming metric have been investigated in [25], [21], [2], [13], [11], [28], [16], [12].…”

Section: Motivation and Related Workmentioning

confidence: 99%

Longest alignment with edits in data streams

Grigorescu

Azer

Zhou

2017

2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Analyzing patterns in data streams generated by network traffic, sensor networks, or satellite feeds is a challenge for systems in which the available storage is limited. In addition, real data is noisy, which makes designing data stream algorithms even more challenging.Motivated by such challenges, we study algorithms for detecting the similarity of two data streams that can be read in sync. Two strings S, T ∈ Σ n form a d-near-alignment if the distance between them in some given metric is at most d.We study the problem of identifying a longest substring of S and T that forms a d-near-alignment under the edit distance, in the simultaneous streaming model. In this model, symbols of strings S and T are streamed at the same time, and the amount of available processing space is sublinear in the length of the strings.We give several algorithms, including an exact one-pass algorithm that uses O d 2 + d log n bits of space. We couple these results with comparable lower bounds.

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Longest common substrings with k mismatches

Cited by 33 publications

References 11 publications

Longest Common Substring with Approximately k Mismatches

Longest Common Substring with Approximately k Mismatches

STAG-CNS: An Order-Aware Conserved Non-coding Sequences Discovery Tool For Arbitrary Numbers of Species

Longest alignment with edits in data streams

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