Exemplar Longest Common Subsequence

Paola Bonizzoni (1) , Gianluca Della Vedova (2) , Riccardo Dondi (3) , Guillaume Fertin (4) , Rafaella Rizzi (1) , Stéphane Vialette (5)

1 DISCo - Dipartimento di Informatica Sistemistica e Comunicazione
2 Dipartimento di Statistica
3 Dipartimento di Scienze dei Linguaggi, della Comunicazione e degli Studi Culturali
4 LINA - Laboratoire d'Informatique de Nantes Atlantique
5 LIGM - Laboratoire d'Informatique Gaspard-Monge

In this paper, we investigate the computational and approximation complexity of the Exemplar Longest Common Subsequence of a set of sequences (ELCS problem), a generalization of the Longest Common Subsequence problem, where the input sequences are over the union of two disjoint sets of symbols, a set of mandatory symbols and a set of optional symbols. We show that different versions of the problem are APX-hard even for instances with two sequences. Moreover, we show that the related problem of determining the existence of a feasible solution of the Exemplar Longest Common Subsequence of two sequences is NP-hard. On the positive side, we first present an efficient algorithm for the ELCS problem over instances of two sequences where each mandatory symbol can appear in total at most three times in the sequences. Furthermore, we present two fixed parameter algorithms for the ELCS problem over instances of two sequences where the parameter is the number of mandatory symbols.

Mots clés: Longest common subsequence; comparative genomics; algorithm design and analysis; combinatorial algorithms; analysis of algorithms and problem complexity.; analysis of algorithms and problem complexity

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]; Algorithme et structure de données [cs.DS]; Complexité [cs.CC]

Paola Bonizzoni, Gianluca Della Vedova, Riccardo Dondi, Guillaume Fertin, Rafaella Rizzi, et al.. Exemplar Longest Common Subsequence. ACM Transactions on Computational Logic, 2007, 4 (4), pp.535-543. ⟨hal-00417728⟩