On the parameterized complexity of the repetition free longest common subsequence problem

Authors:
Guillaume Blin;Paola Bonizzoni;Riccardo Dondi;Florian Sikora
Affiliations:
Université Paris-Est, LIGM UMR CNRS 8049, France;DISCo, Universití degli Studi di Milano-Bicocca, Milano, Italy;Dipartimento di Scienze dei Linguaggi, della Comunicazione e degli Studi Culturali, Universití degli Studi di Bergamo, Via Donizetti 3, 24129 Bergamo, Italy;Université Paris-Est, LIGM UMR CNRS 8049, France and Lehrstuhl für Bioinformatik, Friedrich-Schiller-Universität Jena, Germany
Venue:
Information Processing Letters
Year:
2012

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Abstract

Longest common subsequence is a widely used measure to compare strings, in particular in computational biology. Recently, several variants of the longest common subsequence have been introduced to tackle the comparison of genomes. In particular, the Repetition Free Longest Common Subsequence (RFLCS) problem is a variant of the LCS problem that asks for a longest common subsequence of two input strings with no repetition of symbols. In this paper, we investigate the parameterized complexity of RFLCS. First, we show that the problem does not admit a polynomial kernel. Then, we present a randomized FPT algorithm for the RFLCS problem, improving the time complexity of the existent FPT algorithm.