On the Longest Common Rigid Subsequence Problem
The longest common subsequence problem (LCS) and the closest substring problem (CSP) are two models for the finding of common patterns in strings. The two problem have been studied extensively. The former was previously proved to be not polynomial-time approximable within ratio n δ for a constant δ. The latter was previously proved to be NP-hard and have a PTAS. In this paper, the longest common rigid subsequence problem (LCRS) is studied. LCRS shares similarity with LCS and CSP and has an important application in motif finding in biological sequences. LCRS is proved to be Max-SNP hard in this paper. An exact algorithm with quasi-polynomial average running time is also provided.
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