In this paper, we investigate the computational and approximation complexity of the Exemplar Longest Common Subsequence (ELCS) 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 ELCS 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.

Bonizzoni, P., DELLA VEDOVA, G., Dondi, R., Fertin, G., Rizzi, R., Vialette, S. (2007). Exemplar longest common subsequence. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS, 4(4), 535-543 [10.1109/TCBB.2007.1066].

Exemplar longest common subsequence

BONIZZONI, PAOLA;DELLA VEDOVA, GIANLUCA;RIZZI, RAFFAELLA;
2007

Abstract

In this paper, we investigate the computational and approximation complexity of the Exemplar Longest Common Subsequence (ELCS) 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 ELCS 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.
Articolo in rivista - Articolo scientifico
longest common subsequence; comparative genomics; algorithm design and analysis; combinatorial algorithms; analysis of algorithms; problem complexity
English
535
543
9
Bonizzoni, P., DELLA VEDOVA, G., Dondi, R., Fertin, G., Rizzi, R., Vialette, S. (2007). Exemplar longest common subsequence. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS, 4(4), 535-543 [10.1109/TCBB.2007.1066].
Bonizzoni, P; DELLA VEDOVA, G; Dondi, R; Fertin, G; Rizzi, R; Vialette, S
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/1281
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