Approximated Pattern Matching with the l 1, l 2 and l∞ Metrics

Ohad Lipsky, E. Porat

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Given an alphabet Σ = {1,2,...,|Σ|} text string T ∈ Σ n and a pattern string P ∈ Σ 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 O(1ε2nlogmlog|Σ|)O(1ε2nlog⁡mlog|Σ|) run time. Second, we provide an algorithm that approximates the L  ∞  matching up to a factor of 1 + ε with a run time of O(1εnlogmlog|Σ|)O(1εnlog⁡mlog|Σ|). 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 languageAmerican English
Title of host publicationInternational Symposium on String Processing and Information Retrieval
EditorsAmihood Amir, Andrew Turpin, Alistair Moffat
PublisherSpringer Berlin Heidelberg
StatePublished - 2008

Bibliographical note

Place of conference:Australia

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