On the Parameterized Complexity of the Repetition Free Longest Common Subsequence Problem

Guillaume Blin (1) , Paola Bonizzoni (2) , Riccardo Dondi (3) , Florian Sikora (1, 4)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 DISCo - Dipartimento di Informatica Sistemistica e Comunicazione
3 Dipartimento di Scienze dei Linguaggi, della Comunicazione e degli Studi Culturali
4 Lehrstuhl Bioinformatik Jena

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 with the comparison of genomes. In particular, the Repetition Free Longest Common Subsequence problem (RFLCS) is a variant of the LCS problem that asks for a longest common subsequence problem 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 an FPT algorithm for the RFLCS problem, improving the time complexity of the existent FPT algorithm.

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Guillaume Blin, Paola Bonizzoni, Riccardo Dondi, Florian Sikora. On the Parameterized Complexity of the Repetition Free Longest Common Subsequence Problem. Information Processing Letters, 2012, 112 (7), pp.272-276. ⟨10.1016/j.ipl.2011.12.009⟩. ⟨hal-00637255v2⟩