Approximated pattern matching with the L1, L2 and L metrics

Ohad Lipsky, Ely Porat

Research output: Contribution to journalConference articlepeer-review

8 Scopus citations

Abstract

Given an alphabet ∑ = {1,2,...,|∑|} text string T ∈ ∑n and a pattern string P ∈ ∑ m , for each i = 1,2,...,n - m + 1 define L d (i) as the d-norm distance when the pattern is aligned below the text and starts at position i of the text. The problem of pattern matching with L p distance is to compute L p (i) for every i = 1,2,...,n - m + 1. We discuss the problem for d = 1, ∞. First, in the case of L 1 matching (pattern matching with an L 1 distance) we present an algorithm that approximates the L 1 matching up to a factor of 1 + ε, which has an run time. Second, we provide an algorithm that approximates the L matching up to a factor of 1 + ε with a run time of . We also generalize the problem of String Matching with mismatches to have weighted mismatches and present an O(nlog4 m) algorithm that approximates the results of this problem up to a factor of O(logm) in the case that the weight function is a metric.

Original languageEnglish
Pages (from-to)212-223
Number of pages12
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5280 LNCS
DOIs
StatePublished - 2008
Event15th International Symposium on String Processing and Information Retrieval, SPIRE 2008 - Melbourne. VIC, Australia
Duration: 10 Nov 200812 Nov 2008

Bibliographical note

Funding Information:
Research supported in part by US-Israel Binational Science Foundation.

Funding Information:
★ Research supported in part by US-Israel Binational Science Foundation.

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