Optimal trade-offs for pattern matching with k mismatches

نویسندگان

  • Pawel Gawrychowski
  • Przemyslaw Uznanski
چکیده

Given a pattern of length m and a text of length n, the goal in k-mismatch pattern matching is to compute, for every m-substring of the text, the exact Hamming distance to the pattern or report that it exceeds k. This can be solved in either Õ(n √ k) time as shown by Amir et al. [J. Algorithms 2004] or Õ((m + k) · n/m) time due to a result of Clifford et al. [SODA 2016]. We provide a smooth time trade-off between these two bounds by designing an algorithm working in time Õ((m+ k √ m) · n/m). We complement this with a matching conditional lower bound, showing that a significantly faster combinatorial algorithm is not possible, unless the combinatorial matrix multiplication conjecture fails.

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عنوان ژورنال:
  • CoRR

دوره abs/1704.01311  شماره 

صفحات  -

تاریخ انتشار 2017