Matching with don't-cares and a small number of mismatches

Chaim Linhart, Ron Shamir

Research output: Contribution to journalArticlepeer-review

Abstract

In matching with don't-cares and k mismatches we are given a pattern of length m and a text of length n, both of which may contain don't-cares (a symbol that matches all symbols), and the goal is to find all locations in the text that match the pattern with at most k mismatches, where k is a parameter. We present new algorithms that solve this problem using a combination of convolutions and a dynamic programming procedure. We give randomized and deterministic solutions that run in time O (n k2 log m) and O (n k3 log m), respectively, and are faster than the most efficient extant methods for small values of k. Our deterministic algorithm is the first to obtain an O (polylog (k) ṡ n log m) running time.

Original languageEnglish
Pages (from-to)273-277
Number of pages5
JournalInformation Processing Letters
Volume109
Issue number5
DOIs
StatePublished - 15 Feb 2009

Keywords

  • Analysis of algorithms
  • Approximate wildcard matching
  • Pattern matching

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