Longest common substrings with k mismatches

The longest common substring with k-mismatches problem is to find, given two strings S1 and S2, a longest substring A1 of S1 and A2 of S2 such that the Hamming distance between A1 and A2 is ≤k. We introduce a practical O(nm) time and O(1) space solution for this problem, where n and m are the length...

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Bibliographic Details
Published in:Information processing letters Vol. 115; no. 6-8; pp. 643 - 647
Main Authors: Flouri, Tomas, Giaquinta, Emanuele, Kobert, Kassian, Ukkonen, Esko
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.06.2015
Elsevier Sequoia S.A
Subjects:
Algorithms
Combinatorial problems
Hamming distance
Longest common substring
Mathematical problems
String algorithms
Studies
Vector space
String algorithms
Combinatorial problems
Longest common substring
Hamming distance
ISSN:0020-0190, 1872-6119
Online Access:Get full text
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Summary:The longest common substring with k-mismatches problem is to find, given two strings S1 and S2, a longest substring A1 of S1 and A2 of S2 such that the Hamming distance between A1 and A2 is ≤k. We introduce a practical O(nm) time and O(1) space solution for this problem, where n and m are the lengths of S1 and S2, respectively. This algorithm can also be used to compute the matching statistics with k-mismatches of S1 and S2 in O(nm) time and O(m) space. Moreover, we also present a theoretical solution for the k=1 case which runs in O(nlog⁡m) time, assuming m≤n, and uses O(m) space, improving over the existing O(nm) time and O(m) space bound of Babenko and Starikovskaya [1]. •Two new algorithms for the longest common substring with k mismatches problem.•A practical solution for arbitrary k which uses constant space.•A theoretical solution for one mismatch which runs in quasilinear time.
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ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2015.03.006