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)

Abstract

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.

Keywords

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.

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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

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