Pattern matching with don't cares and few errors

Raphaël Clifford, Klim Efremenko, Ely Porat, Amir Rothschild

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


We present solutions for the k-mismatch pattern matching problem with don't cares. Given a text t of length n and a pattern p of length m with don't care symbols and a bound k, our algorithms find all the places that the pattern matches the text with at most k mismatches. We first give a Θ (n (k + log m log k) log n) time randomised algorithm which finds the correct answer with high probability. We then present a new deterministic Θ (n k2 log2 m) time solution that uses tools originally developed for group testing. Taking our derandomisation approach further we develop an approach based on k-selectors that runs in Θ (n k polylog m) time. Further, in each case the location of the mismatches at each alignment is also given at no extra cost.

Original languageEnglish
Pages (from-to)115-124
Number of pages10
JournalJournal of Computer and System Sciences
Issue number2
StatePublished - 1 Jan 2010
Externally publishedYes


  • Group testing
  • Pattern matching
  • Randomised algorithms
  • String algorithms

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics


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