Hardness of longest common subsequence for sequences with bounded run-lengths

Authors:
Guillaume Blin;Laurent Bulteau;Minghui Jiang;Pedro J. Tejada;Stéphane Vialette
Affiliations:
LIGM, UMR 8049, Université Paris-Est, France;LINA, UMR 6241, Université de Nantes, France;Department of Computer Science, Utah State University;Department of Computer Science, Utah State University;LIGM, UMR 8049, Université Paris-Est, France
Venue:
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Year:
2012

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Abstract

The longest common subsequence (LCS) problem is a classic and well-studied problem in computer science with extensive applications in diverse areas ranging from spelling error corrections to molecular biology. This paper focuses on LCS for fixed alphabet size and fixed run-lengths (i.e., maximum number of consecutive occurrences of the same symbol). We show that LCS is NP-complete even when restricted to (i) alphabets of size 3 and run-length at most 1, and (ii) alphabets of size 2 and run-length at most 2 (both results are tight). For the latter case, we show that the problem is approximable within ratio 3/5.