On the longest common rigid subsequence problem

Nikhil Bansal, Moshe Lewenstein, Bin Ma, Kaizhong Zhang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish
Pages (from-to)270-280
Number of pages11
Issue number2
StatePublished - Feb 2010


  • Approximation algorithms
  • Longest common rigid subsequence
  • Longest common subsequence
  • Motif finding
  • Pattern matching and computational biology


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