Abstract
In this paper, we show that minimal triangulation techniques similar to those proposed by Bouchitté and Todinca can be applied to a variety of perfect phylogeny (or character compatibility) problems. These problems arise in the context of supertree construction, a critical step in estimating the Tree of Life.
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References
Agarwala, R., Fernández-Baca, D.: A polynomial-time algorithm for the perfect phylogeny problem when the number of character states is fixed. SIAM Journal on Computing 23, 1216–1224 (1994)
Berry, A., Bordat, J., Cogis, O.: Generating all the minimal separators of a graph. International Journal of Foundations of Computer Science 11(3), 397–403 (2000)
Bininda-Emonds, O.R.: The evolution of supertrees. Trends in Ecology and Evolution 19(6), 315–322 (2004)
Blair, J., Peyton, B.: An introduction to chordal graphs and clique trees. In: George, J., Gilbert, J., Liu, J.H. (eds.) Graph Theory and Sparse Matrix Computations, IMA Volumes in Mathematics and its Applications, vol. 56, pp. 1–27. Springer (1993)
Bodlaender, H., Heggernes, P., Villanger, Y.: Faster parameterized algorithms for minimum fill–in. Algorithmica 61, 817–838 (2011)
Bodlaender, H., Fellows, M., Warnow, T.: Two strikes against perfect phylogeny. In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 273–283. Springer, Heidelberg (1992)
Bonet, M., Linz, S., John, K.S.: The complexity of finding multiple solutions to betweenness and quartet compatibility. IEEE/ACM Transactions on Computational Biology and Bioinformatics 9(1), 273–285 (2012)
Bordewich, M., Huber, K., Semple, C.: Identifying phylogenetic trees. Discrete Mathematics 300(1-3), 30–43 (2005)
Bouchitté, V., Todinca, I.: Treewidth and minimum fill-in: Grouping the minimal separators. SIAM Journal on Computing 31(1), 212–232 (2001)
Bouchitté, V., Todinca, I.: Listing all potential maximal cliques of a graph. Theoretical Computer Science 276(1-2), 17–32 (2002)
Brinkmeyer, M., Griebel, T., Böcker, S.: Polynomial supertree methods revisited. Advances in Bioinformatics (2011)
Buneman, P.: A characterisation of rigid circuit graphs. Discrete Mathematics 9(3), 205–212 (1974)
Fernández-Baca, D.: The perfect phylogeny problem. In: Cheng, X., Du, D.Z. (eds.) Steiner Trees in Industry, pp. 203–234. Kluwer (2001)
Fomin, F., Kratsch, D., Todinca, I., Villanger, Y.: Exact algorithms for treewidth and minimum fill-in. SIAM Journal on Computing 38(3), 1058–1079 (2008)
Grünewald, S., Huber, K.: Identifying and defining trees. In: Gascuel, O., Steel, M. (eds.) Reconstructing Evolution: New Mathematical and Computational Advances, pp. 217–246. Oxford University Press (2007)
Gusfield, D.: The multi–state perfect phylogeny problem with missing and removable data: solutions via integer–programming and chordal graph theory. Journal of Computational Biology 17(3), 383–399 (2010)
Gysel, R.: Potential maximal clique algorithms for perfect phylogeny problems. Pre-print: arXiv 1303.3931 (2013)
Gysel, R., Gusfield, D.: Extensions and improvements to the chordal graph approach to the multistate perfect phylogeny problem. IEEE/ACM Transactions on Computational Biology and Bioinformatics 8(4), 912–917 (2011)
Habib, M., Stacho, J.: Unique perfect phylogeny is intractable. Theoretical Computer Science 476, 47 – 66 (2013)
Heggernes, P.: Minimal triangulations of graphs: a survey. Discrete Mathematics 306(3), 297–317 (2006)
Hudson, R.: Generating samples under a wright-fisher neutral model of genetic variation. Bioinformatics 18(2), 337–338 (2002)
Kloks, T., Kratsch, D., Spinrad, J.: On treewidth and minimum fill-in of asteroidal triple-free graphs. Theoretical Computer Science 175(2), 309–335 (1997)
McMorris, F., Warnow, T., Wimer, T.: Triangulating vertex–colored graphs. SIAM Journal of Discrete Mathematics 7, 296–306 (1994)
Meacham, C.: Theoretical and computational considerations of the compatibility of qualitative taxonomic characters. In: Felsenstein, J. (ed.) Numerical Taxonomy. NATO ASI Series G, vol. 1, pp. 304–314. Springer (1983)
Parra, A., Scheffler, P.: How to use the minimal separators of a graph for its chordal triangulation. In: Fülöp, Z. (ed.) ICALP 1995. LNCS, vol. 944, pp. 123–134. Springer, Heidelberg (1995)
Parra, A., Scheffler, P.: Characterizations and algorithmic applications of chordal graph embeddings. Discrete Applied Mathematics 79(1-3), 171–188 (1997)
Ross, H., Rodrigo, A.: An assessment of matrix representation with compatibility in supertree construction. In: Bininda-Emonds, O. (ed.) Phylogenetic supertrees: Combining information to reveal the Tree of Life, pp. 35–63. Kluwer Academic Publishers (2004)
Semple, C., Steel, M.: A characterization for a set of partial partitions to define an X-tree. Discrete Mathematics 247(1-3), 169–186 (2002)
Semple, C., Steel, M.: Phylogenetics. In: Oxford Lecture Series in Mathematics and Its Applications. Oxford University Press (2003)
Steel, M.: The complexity of reconstructing trees from qualitative characters and subtrees. Journal of Classification 9(1), 91–116 (1992)
Yannakakis, M.: Computing the minimum fill-in is NP-complete. SIAM Journal on Algebraic Discrete Methods 2, 77–79 (1981)
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Gysel, R. (2014). Minimal Triangulation Algorithms for Perfect Phylogeny Problems. In: Dediu, AH., MartÃn-Vide, C., Sierra-RodrÃguez, JL., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2014. Lecture Notes in Computer Science, vol 8370. Springer, Cham. https://doi.org/10.1007/978-3-319-04921-2_34
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DOI: https://doi.org/10.1007/978-3-319-04921-2_34
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