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Issue No.04 - July/August (2011 vol.8)
pp: 912-917
Rob Gysel , UC Davis, Davis
The multistate perfect phylogeny problem is a classic problem in computational biology. When no perfect phylogeny exists, it is of interest to find a set of characters to remove in order to obtain a perfect phylogeny in the remaining data. This is known as the character removal problem. We show how to use chordal graphs and triangulations to solve the character removal problem for an arbitrary number of states, which was previously unsolved. We outline a preprocessing technique that speeds up the computation of the minimal separators of a graph. Minimal separators are used in our solution to the missing data character removal problem and to Gusfield's solution of the perfect phylogeny problem with missing data.
Perfect phylogeny, chordal graphs, legal triangulations, minimal separators, preprocessing.
Rob Gysel, "Extensions and Improvements to the Chordal Graph Approach to the Multistate Perfect Phylogeny Problem", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.8, no. 4, pp. 912-917, July/August 2011, doi:10.1109/TCBB.2011.27
[1] A. Berry, J.P. Bordat, and O. Cogis, “Generating All the Minimal Separators of a Graph,” Int'l J. Foundations of Computer Science, vol. 11, pp. 397-403, 2000.
[2] J.R.S. Blair and B.W. Peyton, “An Introduction to Chordal Graphs and Clique Trees,” Graph Theory and Sparse Matrix Computations, J.A. George, J.R. Gilbert, and J.W.-H. Liu, eds., IMA Volumes in Math. and Its Applications, vol. 56, pp. 1-27, Springer-Verlag, 1993.
[3] H. Bodlaender, M. Fellows, and T. Warnow, “Two Strikes against Perfect Phylogeny,” Proc. 19th Int'l Colloquium on Automata, Languages, and Programming, pp. 273-283, 1992.
[4] H.L. Bodlaender, “Discovering Treewidth,” Proc. SOFSEM 2005: 31st Ann. Conf. Current Trends in Theory and Practice of Informatics, pp. 1-16, 2005.
[5] V. Bouchitte and I. Todinca, “Listing All Potential Maximal Cliques of a Graph,” Theoretical Computer Science, vol. 276, pp. 17-32, 2002.
[6] P. Buneman, “A Characterization of Rigid Circuit Graphs,” Discrete Math., vol. 9, pp. 205-212, 1974.
[7] R. Diestel, Graduate Texts in Math. 173: Graph Theory. Springer, 2000.
[8] G.A. Dirac, “On Rigid Circuit Graphs,” Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, vol. 25, pp. 71-76, 1961.
[9] J. Felsenstein, Inferring Phylogenies. Sinauer Associates, 2004.
[10] D. Fernandez-Baca, “The Perfect Phylogeny Problem,” Steiner Trees in Industry, D.Z. Du and X. Cheng, eds., pp. 203-234, Kluwer Academic Publishers, 2000.
[11] M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs. Academic Press, 1980.
[12] D. Gusfield, “The Multi-State Perfect Phylogeny Problem with Missing and Removable Data: Solutions via Integer-Programming and Chordal Graph Theory,” J. Computational Biology, vol. 17, no. 3, pp. 383-399, Mar. 2010.
[13] D. Gusfield, Y. Frid, and D. Brown, “Integer Programming Formulations and Computations Solving Phylogenetic and Population Genetic Problems with Missing or Genotypic Data,” Proc. 13th Ann. Int'l Conf. Combinatorics and Computing, pp. 51-64, 2007.
[14] P. Heggernes, “Minimal Triangulation of Graphs: A Survey,” Discrete Math., vol. 306, no. 3, pp. 297-317, 2006.
[15] R. Hudson, “Generating Samples under the Wright-Fisher Neutral Model of Genetic Variation,” Bioinformatics, vol. 18, no. 2, pp. 337-338, 2002.
[16] A. Parra and P. Scheffler, “Characterizations and Algorithmic Applications of Chordal Graph Embeddings,” Discrete Applied Math., vol. 79, pp. 171-188, 1997.
[17] N. Robertson and P.D. Seymour, “Graph Minors III: Planar Tree-Width,” J. Combinatorial Theory (B), vol. 36, pp. 49-64, 1984.
[18] M. Steel, “The Complexity of Reconstructing Trees from Qualitative Characters and Subtrees,” J. Classification, vol 9, pp. 91-116, 1992.
[19] C. Semple and M.A. Steel, Phylogenetics. Oxford Univ. Press, 2003.
[20] K. Takata, “Space-Optimal, Backtracking Algorithms to List the Minimal Vertex Separators of a Graph,” Discrete Applied Math., vol. 158, no. 15, pp. 1660-1667, 2010.
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