Beam-ACO for the Repetition-Free Longest Common Subsequence Problem

  • Christian Blum
  • Maria J. Blesa
  • Borja Calvo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8752)


In this paper we propose a Beam-ACO approach for a combinatorial optimization problem known as the repetition-free longest common subsequence problem. Given two input sequences \(x\) and \(y\) over a finite alphabet \(\varSigma \), this problem concerns to find a longest common subsequence of \(x\) and \(y\) in which no letter is repeated. Beam-ACO algorithms are combinations between the metaheuristic ant colony optimization and a deterministic tree search technique called beam search. The algorithm that we present is an adaptation of a previously published Beam-ACO algorithm for the classical longest common subsequence problem. The results of the proposed algorithm outperform existing heuristics from the literature.



This work was supported by grants TIN2012-37930, TIN2010-14931 and TIN2007-66523 of the Spanish Government, and project 2009-SGR1137 of the Generalitat de Catalunya. In addition, support is acknowledged from IKERBASQUE (Basque Foundation for Science) and the Basque Saiotek and Research Groups 2013-2018 (IT-609-13) programs.


  1. 1.
    Adi, S.S., Braga, M.D.V., Fernandes, C.G., Ferreira, C.E., Martinez, F.V., Sagot, M.F., Stefanes, M.A., Tjandraatmadja, C., Wakabayashi, Y.: Repetition-free longest common subsquence. Disc. Appl. Math. 158, 1315–1324 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Aho, A., Hopcroft, J., Ullman, J.: Data structures and algorithms. Addison-Wesley, Reading (1983)zbMATHGoogle Scholar
  3. 3.
    Blum, C.: Beam-ACO for the longest common subsequence problem. In: Fogel, G., et al. (eds.) Proceedings of CEC 2010 - Congress on Evolutionary Computation, vol. 2. IEEE Press, Piscataway (2010)Google Scholar
  4. 4.
    Blum, C., Dorigo, M.: The hyper-cube framework for ant colony optimization. IEEE Trans. Man Syst. Cybern. - Part B 34(2), 1161–1172 (2004)CrossRefGoogle Scholar
  5. 5.
    Bonizzoni, P., Della Vedova, G.: Variants of constrained longest common subsequence. Inf. Process. Lett. 110(20), 877–881 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Easton, T., Singireddy, A.: A large neighborhood search heuristic for the longest common subsequence problem. J. Heuristics 14(3), 271–283 (2008)CrossRefzbMATHGoogle Scholar
  7. 7.
    Gusfield, D.: Algorithms on Strings, Trees, and Sequences. Computer Science and Computational Biology, Cambridge University Press, Cambridge (1997)CrossRefzbMATHGoogle Scholar
  8. 8.
    Jiang, T., Lin, G., Ma, B., Zhang, K.: A general edit distance between RNA structures. J. Comput. Biol. 9(2), 371–388 (2002)CrossRefGoogle Scholar
  9. 9.
    Julstrom, B.A., Hinkemeyer, B.: Starting from scratch: growing longest common subsequences with evolution. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 930–938. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Maier, D.: The complexity of some problems on subsequences and supersequences. J. ACM 25, 322–336 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Shyu, S.J., Tsai, C.Y.: Finding the longest common subsequence for multiple biological sequences by ant colony optimization. Comput. Oper. Res. 36(1), 73–91 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Smith, T., Waterman, M.: Identification of common molecular subsequences. J. Mol. Biol. 147(1), 195–197 (1981)CrossRefGoogle Scholar
  13. 13.
    Storer, J.: Data Compression: Methods and Theory. Computer Science Press, Rockville (1988)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Computer Science and Artificial IntelligenceUniversity of the Basque CountrySan SebastianSpain
  2. 2.IKERBASQUE, Basque Foundation for ScienceBilbaoSpain
  3. 3.ALBCOM Research GroupUniversitat Politécnica de CatalunyaBarcelonaSpain

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