R.B. Morris, Y. Tsuji, et al.
International Journal for Numerical Methods in Engineering
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. © 2008 Springer Science+Business Media, LLC.
R.B. Morris, Y. Tsuji, et al.
International Journal for Numerical Methods in Engineering
Sankar Basu
Journal of the Franklin Institute
Da-Ke He, Ashish Jagmohan, et al.
ISIT 2007
M. Shub, B. Weiss
Ergodic Theory and Dynamical Systems