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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Vydané v:	Information processing letters Ročník 115; číslo 6-8; s. 643 - 647
Hlavní autori:	Flouri, Tomas, Giaquinta, Emanuele, Kobert, Kassian, Ukkonen, Esko
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 01.06.2015 Elsevier Sequoia S.A
Predmet:	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
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Shrnutí:	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.
Bibliografia:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14
ISSN:	0020-0190 1872-6119
DOI:	10.1016/j.ipl.2015.03.006