TY - JOUR

T1 - On the longest common rigid subsequence problem

AU - Bansal, Nikhil

AU - Lewenstein, Moshe

AU - Ma, Bin

AU - Zhang, Kaizhong

PY - 2010/2

Y1 - 2010/2

N2 - The longest common subsequence problem (LCS) and the closest substring problem (CSP) are two models for finding common patterns in strings, and have been studied extensively. Though both LCS and CSP are NP-Hard, they exhibit very different behavior with respect to polynomial time approximation algorithms. While LCS is hard to approximate within n δ for some δ>0, CSP admits a polynomial time approximation scheme. In this paper, we study the longest common rigid subsequence problem (LCRS). This problem shares similarity with both LCS and CSP and has an important application in motif finding in biological sequences. We show that it is NP-hard to approximate LCRS within ratio n δ, for some constant δ>0, where n is the maximum string length. We also show that it is NP-Hard to approximate LCRS within ratio Ω(m), where m is the number of strings.

AB - The longest common subsequence problem (LCS) and the closest substring problem (CSP) are two models for finding common patterns in strings, and have been studied extensively. Though both LCS and CSP are NP-Hard, they exhibit very different behavior with respect to polynomial time approximation algorithms. While LCS is hard to approximate within n δ for some δ>0, CSP admits a polynomial time approximation scheme. In this paper, we study the longest common rigid subsequence problem (LCRS). This problem shares similarity with both LCS and CSP and has an important application in motif finding in biological sequences. We show that it is NP-hard to approximate LCRS within ratio n δ, for some constant δ>0, where n is the maximum string length. We also show that it is NP-Hard to approximate LCRS within ratio Ω(m), where m is the number of strings.

KW - Approximation algorithms

KW - Longest common rigid subsequence

KW - Longest common subsequence

KW - Motif finding

KW - Pattern matching and computational biology

UR - http://www.scopus.com/inward/record.url?scp=74849124343&partnerID=8YFLogxK

U2 - 10.1007/s00453-008-9175-1

DO - 10.1007/s00453-008-9175-1

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AN - SCOPUS:74849124343

SN - 0178-4617

VL - 56

SP - 270

EP - 280

JO - Algorithmica

JF - Algorithmica

IS - 2

ER -