Pattern matching with don't cares and few errors

Raphaël Clifford; Klim Efremenko; Ely Porat; Amir Rothschild

doi:10.1016/j.jcss.2009.06.002

Pattern matching with don't cares and few errors

Raphaël Clifford, Klim Efremenko, Ely Porat, Amir Rothschild

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

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 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 language	English
Pages (from-to)	115-124
Number of pages	10
Journal	Journal of Computer and System Sciences
Volume	76
Issue number	2
DOIs	https://doi.org/10.1016/j.jcss.2009.06.002
State	Published - Mar 2010

Bibliographical note

Funding Information:
E-mail addresses: [email protected] (R. Clifford), [email protected] (K. Efremenko), [email protected] (E. Porat), [email protected] (A. Rothschild). 1 Research supported in part by the Binational Science Foundation (BSF). 2 Throughout this paper we assume the RAM model with multiplication when giving the time complexity of the FFT. This is in order to be consistent with the large body of previous work on pattern matching with FFTs.

Funding

E-mail addresses: [email protected] (R. Clifford), [email protected] (K. Efremenko), [email protected] (E. Porat), [email protected] (A. Rothschild). 1 Research supported in part by the Binational Science Foundation (BSF). 2 Throughout this paper we assume the RAM model with multiplication when giving the time complexity of the FFT. This is in order to be consistent with the large body of previous work on pattern matching with FFTs.

Funders	Funder number
Engineering and Physical Sciences Research Council	EP/F02682X/1
United States-Israel Binational Science Foundation

Keywords

Group testing
Pattern matching
Randomised algorithms
String algorithms

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10.1016/j.jcss.2009.06.002

Cite this

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title = "Pattern matching with don't cares and few errors",

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 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.",

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author = "Rapha{\"e}l Clifford and Klim Efremenko and Ely Porat and Amir Rothschild",

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Pattern matching with don't cares and few errors

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Keywords

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