Pattern matching with don't cares and few errors

Authors Raphael Clifford, Klim Efremo, Ely Porat, Amir Rotschild



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Author Details

Raphael Clifford
Klim Efremo
Ely Porat
Amir Rotschild

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Raphael Clifford, Klim Efremo, Ely Porat, and Amir Rotschild. Pattern matching with don't cares and few errors. In Search Methodologies. Dagstuhl Seminar Proceedings, Volume 9281, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/DagSemProc.09281.5

Abstract

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 an \Theta(n(k + logmlog k) log n) time randomised algorithm which finds the correct answer with high probability. We then present a new deter- ministic \Theta(nk^2 log^m)time solution that uses tools originally developed for group testing. Taking our derandomisation approach further we de- velop an approach based on k-selectors that runs in \Theta(nk polylogm) time. Further, in each case the location of the mismatches at each alignment is also given at no extra cost.
Keywords
  • Prime Numbers
  • Group Testing
  • Streaming
  • Pattern Matching

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