Complexity Insights of the Minimum Duplication Problem

  • Guillaume Blin
  • Paola Bonizzoni
  • Riccardo Dondi
  • Romeo Rizzi
  • Florian Sikora
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7147)


The Minimum Duplication problem is a well-known problem in phylogenetics and comparative genomics. Given a set of gene trees, the Minimum Duplication problem asks for a species tree that induces the minimum number of gene duplications in the input gene trees. More recently, a variant of the Minimum Duplication problem, called Minimum Duplication Bipartite, has been introduced in [14], where the goal is to find all pre-duplications, that is duplications that precede, in the evolution, the first speciation with respect to a species tree. In this paper, we investigate the complexity of both Minimum Duplication and Minimum Duplication Bipartite problems. First of all, we prove that the Minimum Duplication problem is APX-hard, even when the input consists of five uniquely leaf-labelled gene trees (progressing on the complexity of the problem). Then, we show that the Minimum Duplication Bipartite problem can be solved efficiently by a randomized algorithm when the input gene trees have bounded depth.


Species Tree Gene Duplication Gene Tree Colored Graph Extant Species 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alimonti, P., Kann, V.: Some APX-completeness results for cubic graphs. Theoretical Comput. Sci. 237(1-2), 123–134 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bansal, M.S., Burleigh, J.G., Eulenstein, O., Wehe, A.: Heuristics for the Gene-Duplication Problem: A Θ(n) Speed-Up for the Local Search. In: Speed, T.P., Huang, H. (eds.) RECOMB 2007. LNCS (LNBI), vol. 4453, pp. 238–252. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Bansal, M.S., Eulenstein, O., Wehe, A.: The Gene-Duplication Problem: Near-Linear Time Algorithms for NNI-Based Local Searches. IEEE/ACM Trans. Comput. Biology Bioinform. 6(2), 221–231 (2009)CrossRefGoogle Scholar
  4. 4.
    Bansal, M.S., Shamir, R.: A Note on the Fixed Parameter Tractability of the Gene-Duplication Problem. IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB) 8(3), 848–850 (2011)CrossRefGoogle Scholar
  5. 5.
    Byrka, J., Guillemot, S., Jansson, J.: New results on optimizing rooted triplets consistency. Discrete Appl. Math. 158(11), 1136–1147 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Chang, W.-C., Burleigh, J.G., Fernández-Baca, D.F., Eulenstein, O.: An ILP solution for the gene duplication problem. BMC Bioinformatics (suppl. 1), S14(12) (2011)Google Scholar
  7. 7.
    Chauve, C., El-Mabrouk, N.: New Perspectives on Gene Family Evolution: Losses in Reconciliation and a Link with Supertrees. In: Batzoglou, S. (ed.) RECOMB 2009. LNCS, vol. 5541, pp. 46–58. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Eichler, E.F., Sankoff, D.: Structural dynamics of eukaryotic chromosome evolution. Science 301(5634), 521–565 (2003)CrossRefGoogle Scholar
  9. 9.
    Felsenstein, J.: Phylogenies from molecular sequences: Inference and reliability. Ann. Review Genet. 22, 521–565 (1988)CrossRefGoogle Scholar
  10. 10.
    Fitch, W.M.: Homology a personal view on some of the problems. Trends Genet. 16, 227–231 (2000)CrossRefGoogle Scholar
  11. 11.
    Hallett, M.T., Lagergren, J.: New algorithms for the duplication-loss model. In: RECOMB, pp. 138–146 (2000)Google Scholar
  12. 12.
    Kleinberg, J., Tardos, E.: Algorithm Design. Pearson Education (2006)Google Scholar
  13. 13.
    Ma, B., Li, M., Zhang, L.: From Gene Trees to Species Trees. SIAM J. Comput. 30(3), 729–752 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Ouangraoua, A., Swenson, K.M., Chauve, C.: An Approximation Algorithm for Computing a Parsimonious First Speciation in the Gene Duplication Model. In: Tannier, E. (ed.) RECOMB-CG 2010. LNCS, vol. 6398, pp. 290–301. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    Stege, U.: Gene Trees and Species Trees: The Gene-Duplication Problem in Fixed-Parameter Tractable. In: Dehne, F.K.H.A., Gupta, A., Sack, J.-R., Tamassia, R. (eds.) WADS 1999. LNCS, vol. 1663, pp. 288–293. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  16. 16.
    Welsh, D.J.A., Powell, M.B.: An upper bound for the chromatic number of a graph and its application to timetabling problems. The Computer Journal 10(1), 85–86 (1967)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Guillaume Blin
    • 1
  • Paola Bonizzoni
    • 2
  • Riccardo Dondi
    • 3
  • Romeo Rizzi
    • 4
  • Florian Sikora
    • 1
    • 5
  1. 1.Université Paris-Est, LIGM - UMR CNRS 8049France
  2. 2.DISCoUniversitá degli Studi di Milano-BicoccaMilanoItaly
  3. 3.DSLCSCUniversitá degli Studi di BergamoBergamoItaly
  4. 4.DIMIUniversità di UdineUdineItaly
  5. 5.Lehrstuhl für BioinformatikFriedrich-Schiller-UniversitätJenaGermany

Personalised recommendations