On the Longest Common Rigid Subsequence Problem
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- 作者：Nikhil Bansal ; Moshe Lewenstein ; Bin Ma and Kaizhong Zhang
- 关键词：Longest common subsequence ; Longest common rigid subsequence ; Approximation algorithms ; Motif finding ; Pattern matching and computational biology
- 刊名：Algorithmica
- 出版时间：February, 2010
- 出版年：2010
- 期刊代码：10_0178-4617
- 类别：mat
- 卷：56
- 期：2
- 页码：270-280
- 数据来源：sp
摘要
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.