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On the DCJ Median Problem

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Combinatorial Pattern Matching (CPM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8486))

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Abstract

As many whole genomes are sequenced, comparative genomics is moving from pairwise comparisons to multiway comparisons framed within a phylogenetic tree. A central problem in this process is the inference of data for internal nodes of the tree from data given at the leaves. When phrased as an optimization problem, this problem reduces to computing a median of three genomes under the operations (evolutionary changes) of interest. We focus on the universal rearrangement operation known as double-cut-and join (DCJ) and present three contributions to the DCJ median problem. First, we describe a new strategy to find so-called adequate subgraphs in the multiple breakpoint graph, using a seed genome. We show how to compute adequate subgraphs w.r.t. this seed genome using a network flow formulation. Second, we prove that the upper bound of the median distance computed from the triangle inequality is tight. Finally, we study the question of whether the median distance can reach its lower and upper bounds. We derive a necessary and sufficient condition for the median distance to reach its lower bound and a necessary condition for it to reach its upper bound and design algorithms to test for these conditions.

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Authors and Affiliations

  1. Laboratory for Computational Biology and Bioinformatics, EPFL, Switzerland

    Mingfu Shao & Bernard M. E. Moret

Authors
  1. Mingfu Shao
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  2. Bernard M. E. Moret
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Editor information

Editors and Affiliations

  1. St. Petersburg Department of Steklov Institute of Mathematics, 27 Fontanka, 191023, St. Petersburg, Russia

    Alexander S. Kulikov

  2. National Research University Higher School of Economics, Bldg 3, Bolshoy Trekhsvyatitelskiy pereulok, 109028, Moscow, Russia

    Sergei O. Kuznetsov

  3. University of California at San Diego, 9500 Gilman Drive, EBU3b 4236, 92093-0404, La Jolla, CA, USA

    Pavel Pevzner

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Shao, M., Moret, B.M.E. (2014). On the DCJ Median Problem. In: Kulikov, A.S., Kuznetsov, S.O., Pevzner, P. (eds) Combinatorial Pattern Matching. CPM 2014. Lecture Notes in Computer Science, vol 8486. Springer, Cham. https://doi.org/10.1007/978-3-319-07566-2_28

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  • DOI: https://doi.org/10.1007/978-3-319-07566-2_28

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07565-5

  • Online ISBN: 978-3-319-07566-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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