Mismatch Sampling

Raphaël Clifford; Klim Efremenko; Benny Porat; Ely Porat; Amir Rothschild

doi:10.1016/j.ic.2012.02.007

Mismatch Sampling

Raphaël Clifford, Klim Efremenko, Benny Porat, Ely Porat, Amir Rothschild

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

4 Scopus citations

Abstract

We reconsider the well-known problem of pattern matching under the Hamming distance. Previous approaches have shown how to count the number of mismatches efficiently, especially when a bound is known for the maximum Hamming distance. Our interest is different in that we wish to collect a random sample of mismatches of fixed size at each position in the text. Given a pattern p of length m and a text t of length n, we show how to sample with high probability up to c mismatches from every alignment of p and t in O((c+logn)(n+mlogm)logm) time. Further, we guarantee that the mismatches are sampled uniformly and can therefore be seen as representative of the types of mismatches that occur.

Original language	English
Pages (from-to)	112-118
Number of pages	7
Journal	Information and Computation
Volume	214
DOIs	https://doi.org/10.1016/j.ic.2012.02.007
State	Published - 1 May 2012
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Computer Science Applications
Computational Theory and Mathematics

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10.1016/j.ic.2012.02.007

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title = "Mismatch Sampling",

abstract = "We reconsider the well-known problem of pattern matching under the Hamming distance. Previous approaches have shown how to count the number of mismatches efficiently, especially when a bound is known for the maximum Hamming distance. Our interest is different in that we wish to collect a random sample of mismatches of fixed size at each position in the text. Given a pattern p of length m and a text t of length n, we show how to sample with high probability up to c mismatches from every alignment of p and t in O((c+logn)(n+mlogm)logm) time. Further, we guarantee that the mismatches are sampled uniformly and can therefore be seen as representative of the types of mismatches that occur.",

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

note = "Funding Information: This work was supported in part by the Binational Science Foundation (BSF) grant 2006334 and Israel Science Foundation (ISF) grant 1484/08 as well as the Engineering and Physical Sciences Research Council (EPSRC).",

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AU - Clifford, Raphaël

AU - Efremenko, Klim

AU - Porat, Benny

AU - Porat, Ely

AU - Rothschild, Amir

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N2 - We reconsider the well-known problem of pattern matching under the Hamming distance. Previous approaches have shown how to count the number of mismatches efficiently, especially when a bound is known for the maximum Hamming distance. Our interest is different in that we wish to collect a random sample of mismatches of fixed size at each position in the text. Given a pattern p of length m and a text t of length n, we show how to sample with high probability up to c mismatches from every alignment of p and t in O((c+logn)(n+mlogm)logm) time. Further, we guarantee that the mismatches are sampled uniformly and can therefore be seen as representative of the types of mismatches that occur.

AB - We reconsider the well-known problem of pattern matching under the Hamming distance. Previous approaches have shown how to count the number of mismatches efficiently, especially when a bound is known for the maximum Hamming distance. Our interest is different in that we wish to collect a random sample of mismatches of fixed size at each position in the text. Given a pattern p of length m and a text t of length n, we show how to sample with high probability up to c mismatches from every alignment of p and t in O((c+logn)(n+mlogm)logm) time. Further, we guarantee that the mismatches are sampled uniformly and can therefore be seen as representative of the types of mismatches that occur.

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DO - 10.1016/j.ic.2012.02.007

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VL - 214

SP - 112

EP - 118

JO - Information and Computation

JF - Information and Computation

ER -

Mismatch Sampling

Abstract

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