A Black Box for Online Approximate Pattern Matching

Raphaël Clifford; Klim Efremenko; Benny Porat; Ely Porat

doi:10.1016/j.ic.2010.12.007

A Black Box for Online Approximate Pattern Matching

Raphaël Clifford, Klim Efremenko, Benny Porat, Ely Porat

Department of Computer Science

Bar-Ilan University

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

Abstract

We present a deterministic black box solution for online approximate matching. Given a pattern of length m and a streaming text of length n that arrives one character at a time, the task is to report the distance between the pattern and a sliding window of the text as soon as the new character arrives. Our solution requires O(Σ_j=1log₂mT(n,2 ^j-1)/n) time for each input character, where T(n,m) is the total running time of the best offline algorithm. The types of approximation that are supported include exact matching with wildcards, matching under the Hamming norm, approximating the Hamming norm, k-mismatch and numerical measures such as the L₂ and L₁ norms. For these examples, the resulting online algorithms take O(log²m), O(Σmlogm), O(log ²m/ε²), O(Σklogklogm), O(log²m) and O(Σmlogm) time per character, respectively. The space overhead is linear in the pattern size, which we show is optimal for any deterministic algorithm.

Original language	American English
Pages (from-to)	731-736
Number of pages	6
Journal	Information and Computation
Volume	209
Issue number	4
DOIs	https://doi.org/10.1016/j.ic.2010.12.007
State	Published - 1 Apr 2011

All Science Journal Classification (ASJC) codes

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

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title = "A Black Box for Online Approximate Pattern Matching",

abstract = "We present a deterministic black box solution for online approximate matching. Given a pattern of length m and a streaming text of length n that arrives one character at a time, the task is to report the distance between the pattern and a sliding window of the text as soon as the new character arrives. Our solution requires O(Σj=1log2mT(n,2 j-1)/n) time for each input character, where T(n,m) is the total running time of the best offline algorithm. The types of approximation that are supported include exact matching with wildcards, matching under the Hamming norm, approximating the Hamming norm, k-mismatch and numerical measures such as the L2 and L1 norms. For these examples, the resulting online algorithms take O(log2m), O(Σmlogm), O(log 2m/ε2), O(Σklogklogm), O(log2m) and O(Σmlogm) time per character, respectively. The space overhead is linear in the pattern size, which we show is optimal for any deterministic algorithm.",

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

note = "Funding Information: < This work was partly funded by the BSF, ISF and Google.",

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doi = "10.1016/j.ic.2010.12.007",

language = "American English",

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AU - Clifford, Raphaël

AU - Efremenko, Klim

AU - Porat, Benny

AU - Porat, Ely

N1 - Funding Information: < This work was partly funded by the BSF, ISF and Google.

PY - 2011/4/1

Y1 - 2011/4/1

N2 - We present a deterministic black box solution for online approximate matching. Given a pattern of length m and a streaming text of length n that arrives one character at a time, the task is to report the distance between the pattern and a sliding window of the text as soon as the new character arrives. Our solution requires O(Σj=1log2mT(n,2 j-1)/n) time for each input character, where T(n,m) is the total running time of the best offline algorithm. The types of approximation that are supported include exact matching with wildcards, matching under the Hamming norm, approximating the Hamming norm, k-mismatch and numerical measures such as the L2 and L1 norms. For these examples, the resulting online algorithms take O(log2m), O(Σmlogm), O(log 2m/ε2), O(Σklogklogm), O(log2m) and O(Σmlogm) time per character, respectively. The space overhead is linear in the pattern size, which we show is optimal for any deterministic algorithm.

AB - We present a deterministic black box solution for online approximate matching. Given a pattern of length m and a streaming text of length n that arrives one character at a time, the task is to report the distance between the pattern and a sliding window of the text as soon as the new character arrives. Our solution requires O(Σj=1log2mT(n,2 j-1)/n) time for each input character, where T(n,m) is the total running time of the best offline algorithm. The types of approximation that are supported include exact matching with wildcards, matching under the Hamming norm, approximating the Hamming norm, k-mismatch and numerical measures such as the L2 and L1 norms. For these examples, the resulting online algorithms take O(log2m), O(Σmlogm), O(log 2m/ε2), O(Σklogklogm), O(log2m) and O(Σmlogm) time per character, respectively. The space overhead is linear in the pattern size, which we show is optimal for any deterministic algorithm.

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DO - 10.1016/j.ic.2010.12.007

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EP - 736

JO - Information and Computation

JF - Information and Computation

IS - 4

ER -

A Black Box for Online Approximate Pattern Matching

Abstract

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