ar X iv : 1 40 9 . 16 94 v 2 [ cs . D S ] 1 6 M ar 2 01 5 Longest common substrings with k mismatches

نویسندگان

  • Tomas Flouri
  • Emanuele Giaquinta
  • Kassian Kobert
  • Esko Ukkonen
چکیده

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(n logm) 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].

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تاریخ انتشار 2015