TY - JOUR

T1 - On the longest common parameterized subsequence

AU - Keller, Orgad

AU - Kopelowitz, Tsvi

AU - Lewenstein, Moshe

PY - 2009/11/28

Y1 - 2009/11/28

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70350012270&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2009.09.011

DO - 10.1016/j.tcs.2009.09.011

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AN - SCOPUS:70350012270

SN - 0304-3975

VL - 410

SP - 5347

EP - 5353

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 51

ER -