DagSemProc.09281.5.pdf
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Pattern matching with don't cares and few errors
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- Publication date: 2009-11-10
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Creative Commons Attribution 4.0 International license
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Volume:
Dagstuhl Seminar Proceedings, Volume 9281
Series: Dagstuhl Seminar Proceedings (DagSemProc)
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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
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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