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Complexity Insights of the Minimum Duplication Problem

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SOFSEM 2012: Theory and Practice of Computer Science (SOFSEM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

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Author information

Authors and Affiliations

  1. Université Paris-Est, LIGM - UMR CNRS 8049, France

    Guillaume Blin & Florian Sikora

  2. DISCo, Universitá degli Studi di Milano-Bicocca, Milano, Italy

    Paola Bonizzoni

  3. DSLCSC, Universitá degli Studi di Bergamo, Bergamo, Italy

    Riccardo Dondi

  4. DIMI, Università di Udine, Udine, Italy

    Romeo Rizzi

  5. Lehrstuhl für Bioinformatik, Friedrich-Schiller-Universität, Jena, Germany

    Florian Sikora

Authors
  1. Guillaume Blin
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  2. Paola Bonizzoni
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  3. Riccardo Dondi
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  4. Romeo Rizzi
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  5. Florian Sikora
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Editor information

Editors and Affiliations

  1. Faculty of Informatics and Information Technologies, Institute of Informatics and Software Engineering, Slovak University of Technology in Bratislava, Ilkovičova 3, 842 16, Bratislava 4, Slovakia

    Mária Bieliková

  2. Dept. of Intelligent Systems and Business Informatics, Alpen-Adria-Universität Klagenfurt, Universitätsstr. 65-57, 9020, Klagenfurt, Austria

    Gerhard Friedrich

  3. Department of Computer Science, University of Oxford, UK

    Georg Gottlob

  4. Security Engineering Group, Technische Universität Darmstadt, Hochschulstr. 10, 64289, Darmstadt, Germany

    Stefan Katzenbeisser

  5. University of Illinois at Chicago, Dept. of Math., Stat. and Comp. Sci, 851 S. Morgan Street, Chicago, IL 60607-7045, USA; and University of Szeged, Research Group on Artificial Intelligence of the Hungarian Academy of Sciences, 6701 Szeged, Postafiók, Hungary

    György Turán

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© 2012 Springer-Verlag Berlin Heidelberg

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Blin, G., Bonizzoni, P., Dondi, R., Rizzi, R., Sikora, F. (2012). Complexity Insights of the Minimum Duplication Problem. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds) SOFSEM 2012: Theory and Practice of Computer Science. SOFSEM 2012. Lecture Notes in Computer Science, vol 7147. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27660-6_13

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  • DOI: https://doi.org/10.1007/978-3-642-27660-6_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27659-0

  • Online ISBN: 978-3-642-27660-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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