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 -