On the longest common parameterized subsequence

Orgad Keller, Tsvi Kopelowitz, Moshe Lewenstein

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

The well-known problem of the longest common subsequence (LCS), of two strings of lengths n and m respectively, is O (n m)-time solvable and is a classical distance measure for strings. Another well-studied string comparison measure is that of parameterized matching, where two equal-length strings are a parameterized match if there exists a bijection on the alphabets such that one string matches the other under the bijection. All works associated with parameterized pattern matching present polynomial time algorithms. There have been several attempts to accommodate parameterized matching along with other distance measures, as these turn out to be natural problems, e.g., Hamming distance, and a bounded version of edit-distance. Several algorithms have been proposed for these problems. In this paper we consider the longest common parameterized subsequence problem which combines the LCS measure with parameterized matching. We prove that the problem is NP-hard, and then show a couple of approximation algorithms for the problem.

Original languageEnglish
Pages (from-to)5347-5353
Number of pages7
JournalTheoretical Computer Science
Volume410
Issue number51
DOIs
StatePublished - 28 Nov 2009

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