Pattern matching with don't cares and few errors

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...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 76; no. 2; pp. 115 - 124
Main Authors: Clifford, Raphaël, Efremenko, Klim, Porat, Ely, Rothschild, Amir
Format: Journal Article
Language:English
Published: Elsevier Inc 01.03.2010
Subjects:
Algorithms
Alignment
Errors
Group testing
Matching
Mathematical models
Pattern matching
Position (location)
Randomised algorithms
String algorithms
Symbols
Texts
Randomised algorithms
String algorithms
Group testing
Pattern matching
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary: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 k 2 log 2 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.
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ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2009.06.002