Abstract
A MUL-tree is a generalization of a phylogenetic tree that allows the same leaf label to be used many times. Lott et al. [9,10] recently introduced the problem of inferring a so-called consensus MUL-tree from a set of conflicting MUL-trees and gave an exponential-time algorithm for a special greedy variant. Here, we study strict and majority rule consensus MUL-trees, and present the first ever polynomial-time algorithms for building a consensus MUL-tree. We give a simple, fast algorithm for building a strict consensus MUL-tree. We also show that although it is NP-hard to find a majority rule consensus MUL-tree, the variant which we call the singular majority rule consensus MUL-tree is unique and can be constructed efficiently.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aho, A.V., Sagiv, Y., Szymanski, T.G., Ullman, J.D.: Inferring a tree from lowest common ancestors with an application to the optimization of relational expressions. SIAM Journal on Computing 10, 405–421 (1981)
Day, W.H.E.: Optimal algorithms for comparing trees with labeled leaves. Journal of Classification 2(1), 7–28 (1985)
Felsenstein, J.: Inferring Phylogenies. Sinauer Associates, Inc., Sunderland (2004)
Ganapathy, G., Goodson, B., Jansen, R., Le, H.-S., Ramachandran, V., Warnow, T.: Pattern identification in biogeography. IEEE/ACM Transactions on Computational Biology and Bioinformatics 3(4), 334–346 (2006)
Garey, M., Johnson, D.: Computers and Intractability – A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York (1979)
Guillemot, S., Jansson, J., Sung, W.-K.: Computing a smallest multilabeled phylogenetic tree from rooted triplets. IEEE/ACM Transactions on Computational Biology and Bioinformatics 8(4), 1141–1147 (2011)
Huber, K.T., Lott, M., Moulton, V., Spillner, A.: The complexity of deriving multi-labeled trees from bipartitions. J. of Comp. Biology 15(6), 639–651 (2008)
Huber, K.T., Spillner, A., Suchecki, R., Moulton, V.: Metrics on multilabeled trees: Interrelationships and diameter bounds. IEEE/ACM Transactions on Computational Biology and Bioinformatics 8(4), 1029–1040 (2011)
Lott, M., Spillner, A., Huber, K.T., Moulton, V.: PADRE: a package for analyzing and displaying reticulate evolution. Bioinformatics 25(9), 1199–1200 (2009)
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)
Margush, T., McMorris, F.R.: Consensus n-Trees. Bulletin of Mathematical Biology 43(2), 239–244 (1981)
Nelson, G., Platnick, N.: Systematics and Biogeography: Cladistics and Vicariance. Columbia University Press (1981)
Page, R.D.M.: Parasites, phylogeny and cospeciation. International Journal for Parasitology 23, 499–506 (1993)
Page, R.D.M.: Maps between trees and cladistic analysis of historical associations among genes, organisms, and areas. Systematic Biology 43(1), 58–77 (1994)
Scornavacca, C., Berry, V., Ranwez, V.: Building species trees from larger parts of phylogenomic databases. Information and Computation 209(3), 590–605 (2011)
Sokal, R.R., Rohlf, F.J.: Taxonomic congruence in the Leptopodomorpha re-examined. Systematic Zoology 30(3), 309–325 (1981)
Sung, W.-K.: Algorithms in Bioinformatics: A Practical Introduction. Chapman & Hall/CRC (2010)
Wareham, H.T.: An efficient algorithm for computing Mi consensus trees. B.Sc. Honours thesis, Memorial University of Newfoundland, Canada (1985)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cui, Y., Jansson, J., Sung, WK. (2011). Algorithms for Building Consensus MUL-trees. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_76
Download citation
DOI: https://doi.org/10.1007/978-3-642-25591-5_76
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25590-8
Online ISBN: 978-3-642-25591-5
eBook Packages: Computer ScienceComputer Science (R0)