Skip to main content
SpringerLink
Log in

Algorithms for the Majority Rule (+) Consensus Tree and the Frequency Difference Consensus Tree

  • Conference paper
Algorithms in Bioinformatics (WABI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 8126))

Included in the following conference series:

  • 2053 Accesses

Abstract

This paper presents two new deterministic algorithms for constructing consensus trees. Given an input of k phylogenetic trees with identical leaf label sets and n leaves each, the first algorithm constructs the majority rule (+) consensus tree in O(k n) time, which is optimal since the input size is Ω(k n), and the second one constructs the frequency difference consensus tree in min {O(k n 2), O(k n (k + log2 n))} time.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adams III, E.N.: Consensus techniques and the comparison of taxonomic trees. Systematic Zoology 21(4), 390–397 (1972)

    Article  Google Scholar 

  2. Amenta, N., Clarke, F., St. John, K.: A linear-time majority tree algorithm. In: Benson, G., Page, R.D.M. (eds.) WABI 2003. LNCS (LNBI), vol. 2812, pp. 216–227. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  3. Barthélemy, J.-P., McMorris, F.R.: The median procedure for n-trees. Journal of Classification 3(2), 329–334 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bremer, K.: Combinable component consensus. Cladistics 6(4), 369–372 (1990)

    Article  MathSciNet  Google Scholar 

  5. Bryant, D.: A classification of consensus methods for phylogenetics. In: Janowitz, M.F., Lapointe, F.-J., McMorris, F.R., Mirkin, B., Roberts, F.S. (eds.) Bioconsensus. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 61, pp. 163–184. American Mathematical Society (2003)

    Google Scholar 

  6. Cole, R., Farach-Colton, M., Hariharan, R., Przytycka, T., Thorup, M.: An O(n logn) algorithm for the maximum agreement subtree problem for binary trees. SIAM Journal on Computing 30(5), 1385–1404 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cotton, J.A., Wilkinson, M.: Majority-rule supertrees. Systematic Biology 56(3), 445–452 (2007)

    Article  Google Scholar 

  8. Cui, Y., Jansson, J., Sung, W.-K.: Polynomial-time algorithms for building a consensus MUL-tree. Journal of Computational Biology 19(9), 1073–1088 (2012)

    Article  MathSciNet  Google Scholar 

  9. Day, W.H.E.: Optimal algorithms for comparing trees with labeled leaves. Journal of Classification 2(1), 7–28 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  10. Degnan, J.H., DeGiorgio, M., Bryant, D., Rosenberg, N.A.: Properties of consensus methods for inferring species trees from gene trees. Systematic Biology 58(1), 35–54 (2009)

    Article  Google Scholar 

  11. Dong, J., Fernández-Baca, D., McMorris, F.R., Powers, R.C.: Majority-rule (+) consensus trees. Mathematical Biosciences 228(1), 10–15 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  13. Felsenstein, J.: PHYLIP, version 3.6. Software package, Department of Genome Sciences. University of Washington, Seattle (2005)

    Google Scholar 

  14. Goloboff, P.A., Farris, J.S., Källersjö, M., Oxelman, B., Ramírez, M.J., Szumik, C.A.: Improvements to resampling measures of group support. Cladistics 19(4), 324–332 (2003)

    Article  Google Scholar 

  15. Goloboff, P.A., Farris, J.S., Nixon, K.C.: TNT, a free program for phylogenetic analysis. Cladistics 24(5), 774–786 (2008)

    Article  Google Scholar 

  16. Holder, M.T., Sukumaran, J., Lewis, P.O.: A justification for reporting the majority-rule consensus tree in Bayesian phylogenetics. Systematic Biology 57(5), 814–821 (2008)

    Article  Google Scholar 

  17. Jansson, J., Shen, C., Sung, W.-K.: Improved algorithms for constructing consensus trees. In: Proceedings of SODA 2013, pp. 1800–1813. SIAM (2013)

    Google Scholar 

  18. Jansson, J., Shen, C., Sung, W.-K.: An optimal algorithm for building the majority rule consensus tree. In: Deng, M., Jiang, R., Sun, F., Zhang, X. (eds.) RECOMB 2013. LNCS, vol. 7821, pp. 88–99. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  19. Jansson, J., Sung, W.-K.: Constructing the R* consensus tree of two trees in subcubic time. Algorithmica 66(2), 329–345 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  20. Lott, M., Spillner, A., Huber, K.T., Petri, A., Oxelman, B., Moulton, V.: Inferring polyploid phylogenies from multiply-labeled gene trees. BMC Evolutionary Biology 9, 216 (2009)

    Article  Google Scholar 

  21. Margush, T., McMorris, F.R.: Consensus n-Trees. Bulletin of Mathematical Biology 43(2), 239–244 (1981)

    MathSciNet  MATH  Google Scholar 

  22. McMorris, F.R., Powers, R.C.: A characterization of majority rule for hierarchies. Journal of Classification 25(2), 153–158 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  23. Page, R.: COMPONENT, version 2.0. Software package, University of Glasgow, U.K. (1993)

    Google Scholar 

  24. Ronquist, F., Huelsenbeck, J.P.: MrBayes 3: Bayesian phylogenetic inference under mixed models. Bioinformatics 19(12), 1572–1574 (2003)

    Article  Google Scholar 

  25. Sokal, R.R., Rohlf, F.J.: Taxonomic congruence in the Leptopodomorpha re-examined. Systematic Zoology 30(3), 309–325 (1981)

    Article  Google Scholar 

  26. Sukumaran, J., Holder, M.T.: DendroPy: A Python library for phylogenetic computing. Bioinformatics 26(12), 1569–1571 (2010)

    Article  Google Scholar 

  27. Sung, W.-K.: Algorithms in Bioinformatics: A Practical Introduction. Chapman & Hall/CRC (2010)

    Google Scholar 

  28. Swofford, D.L.: PAUP*, version 4.0. Software package. Sinauer Associates, Inc., Sunderland (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Jesper Jansson

  2. Stanford University, 450 Serra Mall, Stanford, CA, 94305-2004, USA

    Chuanqi Shen

  3. School of Computing, National University of Singapore, 13 Computing Drive, Singapore, 117417

    Wing-Kin Sung

  4. Genome Institute of Singapore, 60 Biopolis Street, Genome, Singapore, 138672

    Wing-Kin Sung

Authors
  1. Jesper Jansson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chuanqi Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wing-Kin Sung
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. ithree institute,, University of Technology Sydney, 2007, Ultimo, NSW, Australia

    Aaron Darling

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

    Jens Stoye

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jansson, J., Shen, C., Sung, WK. (2013). Algorithms for the Majority Rule (+) Consensus Tree and the Frequency Difference Consensus Tree. In: Darling, A., Stoye, J. (eds) Algorithms in Bioinformatics. WABI 2013. Lecture Notes in Computer Science(), vol 8126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40453-5_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-40453-5_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40452-8

  • Online ISBN: 978-3-642-40453-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation