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A Sublinear-Time Randomized Approximation Scheme for the Robinson-Foulds Metric

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Research in Computational Molecular Biology (RECOMB 2006)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 3909))

Abstract

The Robinson-Foulds (RF) metric is the measure most widely used in comparing phylogenetic trees; it can be computed in linear time using Day’s algorithm. When faced with the need to compare large numbers of large trees, however, even linear time becomes prohibitive. We present a randomized approximation scheme that provides, with high probability, a (1+ε) approximation of the true RF metric for all pairs of trees in a given collection. Our approach is to use a sublinear-space embedding of the trees, combined with an application of the Johnson-Lindenstrauss lemma to approximate vector norms very rapidly. We discuss the consequences of various parameter choices (in the embedding and in the approximation requirements). We also implemented our algorithm as a Java class that can easily be combined with popular packages such as Mesquite; in consequence, we present experimental results illustrating the precision and running-time tradeoffs as well as demonstrating the speed of our approach.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of New Mexico, Albuquerque, NM, 87131, USA

    Nicholas D. Pattengale & Bernard M. E. Moret

Authors
  1. Nicholas D. Pattengale
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  2. Bernard M. E. Moret
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Editor information

Editors and Affiliations

  1. Georgia Institute of Technology and Università di Padova,  

    Alberto Apostolico

  2. Topic Chairs, P.O. Box

    Concettina Guerra

  3. Center for Molecular Biology and Computer Sciecne Department, Brown University, 115 Waterman St., 02912, Providence, RI, USA

    Sorin Istrail

  4. University of California, San Diego, USA

    Pavel A. Pevzner

  5. Department of Molecular and Computational Biology, University of Southern California, 1050 Childs Way, 90089-2910, Los Angeles, CA, USA

    Michael Waterman

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© 2006 Springer-Verlag Berlin Heidelberg

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Pattengale, N.D., Moret, B.M.E. (2006). A Sublinear-Time Randomized Approximation Scheme for the Robinson-Foulds Metric. In: Apostolico, A., Guerra, C., Istrail, S., Pevzner, P.A., Waterman, M. (eds) Research in Computational Molecular Biology. RECOMB 2006. Lecture Notes in Computer Science(), vol 3909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11732990_19

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  • DOI: https://doi.org/10.1007/11732990_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33295-4

  • Online ISBN: 978-3-540-33296-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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