Exemplar Longest Common Subsequence

  • Paola Bonizzoni
  • Gianluca Della Vedova
  • Riccardo Dondi
  • Guillaume Fertin
  • Stéphane Vialette
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3992)

Abstract

In the 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, efficient algorithms for the ELCS problem over instances of two sequences where each mandatory symbol can appear totally at most three times or the number of mandatory symbols is bounded by a constant are given.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Paola Bonizzoni
    • 1
  • Gianluca Della Vedova
    • 2
  • Riccardo Dondi
    • 1
  • Guillaume Fertin
    • 3
  • Stéphane Vialette
    • 4
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano-Bicocca MilanoItaly
  2. 2.Dipartimento di StatisticaUniversità degli Studi di Milano-Bicocca MilanoItaly
  3. 3.LINA – FRE CNRS 2729Université de NantesNantes Cedex 3France
  4. 4.LRI – UMR CNRS 8623 Faculté des Sciences d’OrsayUniversité Paris-Sud Bât 490Orsay CedexFrance

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