title: Exemplar longest common subsequence.
abstract: 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.
authors.affiliation: Dipartimento di Informatica, Sistemistica e Communicazione, Universitá degli Studi di Milano-Bicocca, Via Bicocca Degli, Arcimboldi, Milano, Italy. bonizzoni@disco.unimib.it
authors.forename: Paola
authors.initials: P
authors.lastname: Bonizzoni
authors.forename: Gianluca
authors.initials: G
authors.lastname: Della Vedova
authors.forename: Riccardo
authors.initials: R
authors.lastname: Dondi
authors.forename: Guillaume
authors.initials: G
authors.lastname: Fertin
authors.forename: Raffaella
authors.initials: R
authors.lastname: Rizzi
authors.forename: Stéphane
authors.initials: S
authors.lastname: Vialette
mesh_terms: D000465:Algorithms; D019295:Computational Biology / Q000379:methods*; D003201:Computers; D003627:Data Interpretation, Statistical; D015233:Models, Statistical; D008962:Models, Theoretical; D017422:Sequence Analysis, DNA; D012984:Software