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Computing the Rooted Triplet Distance between Galled Trees by Counting Triangles

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Combinatorial Pattern Matching (CPM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7354))

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Abstract

We consider a generalization of the rooted triplet distance between two phylogenetic trees to two phylogenetic networks. We show that if each of the two given phylogenetic networks is a so-called galled tree with n leaves then the rooted triplet distance can be computed in o(n 2.688) time. Our upper bound is obtained by reducing the problem of computing the rooted triplet distance to that of counting monochromatic and almost- monochromatic triangles in an undirected, edge-colored graph. To count different types of colored triangles in a graph efficiently, we extend an existing technique based on matrix multiplication and obtain several new related results that may be of independent interest.

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References

  1. Alon, N., Yuster, R., Zwick, U.: Finding and counting given length cycles. Algorithmica 17(3), 209–223 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bansal, M.S., Dong, J., Fernández-Baca, D.: Comparing and aggregating partially resolved trees. Theoretical Computer Science 412(48), 6634–6652 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chan, H.-L., Jansson, J., Lam, T.-W., Yiu, S.-M.: Reconstructing an ultrametric galled phylogenetic network from a distance matrix. Journal of Bioinformatics and Computational Biology 4(4), 807–832 (2006)

    Article  Google Scholar 

  4. Choy, C., Jansson, J., Sadakane, K., Sung, W.-K.: Computing the maximum agreement of phylogenetic networks. Theoretical Computer Science 335(1), 93–107 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Coppersmith, D., Winograd, S.: Matrix Multiplication via Arithmetic Progressions. Journal of Symbolic Computation 9, 251–280 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  6. Critchlow, D.E., Pearl, D.K., Qian, C.: The triples distance for rooted bifurcating phylogenetic trees. Systematic Biology 45(3), 323–334 (1996)

    Article  Google Scholar 

  7. Felsenstein, J.: Inferring Phylogenies. Sinauer Associates, Inc., Sunderland (2004)

    Google Scholar 

  8. Gusfield, D., Eddhu, S., Langley, C.: Optimal, efficient reconstruction of phylogenetic networks with constrained recombination. Journal of Bioinformatics and Computational Biology 2(1), 173–213 (2004)

    Article  Google Scholar 

  9. Harel, D., Tarjan, R.E.: Fast algorithms for finding nearest common ancestors. SIAM Journal on Computing 13(2), 338–355 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  10. Huson, D.H., Rupp, R., Scornavacca, C.: Phylogenetic Networks: Concepts, Algorithms and Applications. Cambridge University Press (2010)

    Google Scholar 

  11. van Iersel, L., Kelk, S.: Constructing the Simplest Possible Phylogenetic Network from Triplets. Algorithmica 60(2), 207–235 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Jansson, J., Nguyen, N.B., Sung, W.-K.: Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network. SIAM Journal on Computing 35(5), 1098–1121 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Morrison, D.: Introduction to Phylogenetic Networks. RJR Productions (2011)

    Google Scholar 

  14. Nakhleh, L., Warnow, T., Ringe, D., Evans, S.N.: A comparison of phylogenetic reconstruction methods on an Indo-European dataset. Transactions of the Philological Society 103(2), 171–192 (2005)

    Article  Google Scholar 

  15. Nielsen, J., Kristensen, A.K., Mailund, T., Pedersen, C.N.S.: A sub-cubic time algorithm for computing the quartet distance between two general trees. Algorithms for Molecular Biology 6, Article 15 (2011)

    Google Scholar 

  16. Stothers, A.J.: On the Complexity of Matrix Multiplication. PhD thesis, University of Edinburgh (2010)

    Google Scholar 

  17. Tarjan, R.E.: Applications of path compression on balanced trees. Journal of the ACM 26(4), 690–715 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wang, L., Ma, B., Li, M.: Fixed topology alignment with recombination. Discrete Applied Mathematics 104(1-3), 281–300 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  19. Vassilevska, V., Williams, R., Yuster, R.: Finding Heaviest H-Subgraphs in Real Weighted Graphs, with Applications. ACM Transactions on Algorithms 6(3), Article 44 (2010)

    Google Scholar 

  20. Vassilevska Williams, V.: Breaking the Coppersmith-Winograd barrier. UC Berkely and Stanford University (2011) (manuscript)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Mathematical Bioinformatics, Institute for Chemical Research, Kyoto University, Gokasho, Uji, Kyoto, 611-0011, Japan

    Jesper Jansson

  2. Department of Computer Science, Lund University, 22100, Lund, Sweden

    Andrzej Lingas

Authors
  1. Jesper Jansson
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  2. Andrzej Lingas
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Helsinki, Gustaf Hällström Katu 2b, P.O. Box 68, 00014, Helsinki, Finland

    Juha Kärkkäinen

  2. Faculty of Technology, University of Bielefeld, Universitätsstraße 25, 33615, Bielefeld, Germany

    Jens Stoye

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© 2012 Springer-Verlag Berlin Heidelberg

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Jansson, J., Lingas, A. (2012). Computing the Rooted Triplet Distance between Galled Trees by Counting Triangles. In: Kärkkäinen, J., Stoye, J. (eds) Combinatorial Pattern Matching. CPM 2012. Lecture Notes in Computer Science, vol 7354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31265-6_31

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  • DOI: https://doi.org/10.1007/978-3-642-31265-6_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31264-9

  • Online ISBN: 978-3-642-31265-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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