Algorithms for computing the longest parameterized common subsequence

Authors:
Costas S. Iliopoulos;Marcin Kubica;M. Sohel Rahman;Tomasz Waleń
Affiliations:
Algorithm Design Group, Department of Computer Science, Kings College London, London, England;Institute of Informatics, Warsaw University, Warszawa, Poland;Algorithm Design Group, Department of Computer Science, Kings College London, London, England;Institute of Informatics, Warsaw University, Warszawa, Poland
Venue:
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Year:
2007

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Abstract

In this paper, we revisit the classic and well-studied longest common subsequence (LCS) problem and study some new variants, first introduced and studied by Rahman and Iliopoulos [Algorithms for Computing Variants of the Longest Common Subsequence Problem, ISAAC 2006]. Here we define a generalization of these variants, the longest parameterized common subsequence (LPCS) problem, and show how to solve it in O(n2) and O(n+Rlog n) time. Furthermore, we show how to compute two variants of LCS, RELAG and RIFIG in O(n + R) time.