Abstract
In [3,2], the authors introduced the Generalised Cladistic Character Compatibility (GCCC) Problem which generalises a variant of the Perfect Phylogeny Problem in order to model better experiments in molecular biology showing that genes contain information for currently unexpressed traits, e.g., having teeth. In [3], the authors show that this problem is NP-complete and give some special cases which are polynomial. The authors also pose an open case of this problem where each character has only one generalised state, and each character tree is non-branching, a case that models these experiments particularly closely, which we call the Benham-Kannan-Warnow (BKW) Case.
In [18], the authors study the complexity of a set of cases of the GCCC Problem for non-branching character trees when the phylogeny tree that is a solution to this compatibility problem is restricted to be either a tree, path or single-branch tree. In particular, they show that if the phylogeny tree must have only one branch, the BKW Case is polynomial-time solvable, by giving a novel algorithm based on PQ-trees used for the consecutive-ones property of binary matrices.
In this work, we characterise the complexity of the remainder of the cases considered in [18] for the single-branch tree and the path. We show that some of the open cases are polynomial-time solvable, one by using an algorithm based on directed paths in the character trees similar to the algorithm in [2], and the second by showing that this case can be reduced to a polynomial-time solvable case of [18]. On the other hand, we will show that other open cases are NP-complete using an interesting variation of the ordering problems we study here. In particular, we show that the BKW Case for the path is NP-complete.
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References
Agarwala, R., Fernandez-Baca, D.: A polynomial-time algorithm for the perfect phylogeny problem when the number of character states is fixed. SIAM J. Computing 26(6), 1216–1224 (1994)
Benham, C., Kannan, S., Paterson, M., Warnow, T.: Hen’s teeth and whale’s feet: Generalized characters and their compatibility. J. Computational Biology 2(4), 515–525 (1995)
Benham, C., Kannan, S., Warnow, T.: Of chicken teeth and mouse eyes, or generalized character compatibility. In: Galil, Z., Ukkonen, E. (eds.) CPM 1995. LNCS, vol. 937, pp. 17–26. Springer, Heidelberg (1995)
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)
Booth, K.S., Lueker, G.S.: Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. J. Computer and System Sciences 13(3), 335–379 (1976)
Estabrook, G., McMorris, F.: When is one estimate of evolutionary relationships a refinement of the another? J. Mathematical Biology 10, 327–373 (1980)
Felsenstein, J.: Numerical methods for inferring evolutionary trees. The Quarterly Review of Biology 57(4), 379–404 (1982)
Figuera, L., Pandolfo, M., Dunne, P., Cantu, J., Patel, P.: Mapping the congenital generalized hypertrichosis locus to chromosome Xq24-q27.1. Nature 10, 202–207 (1995)
Fulkerson, D., Gross, O.: Incidence matrices and interval graphs. Pacific J. Mathematics 15, 835–855 (1965)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)
Gramm, J., Nierhoff, T., Sharan, R., Tantau, T.: Haplotyping with missing data via perfect path phylogenies. Discrete Applied Mathematics 155, 788–805 (2007)
Gusfield, D.: Efficient algorithms for inferring evolutionary trees. Networks 21, 19–28 (1991)
Gusfield, D.: The multi-state perfect phylogeny problem with missing and removable data: Solutions via integer-programming and chordal graph theory. In: Batzoglou, S. (ed.) RECOMB 2009. LNCS, vol. 5541, pp. 236–252. Springer, Heidelberg (2009)
Janis, C.: The sabertooth’s repeat performances. Natural History 103, 78–82 (1994)
Kannan, S., Warnow, T.: Inferring evolutionary history from DNA sequences. SIAM J. Computing 23(4), 713–737 (1994)
Kannan, S., Warnow, T.: A fast algorithm for the computation and enumeration of perfect phylogenies. In: Proc. of SODA 1995, pp. 595–603 (1995)
Kollar, E., Fisher, C.: Tooth induction in chick epithelium: Expression of quiescent genes for enamel synthesis. Science 207, 993–995 (1980)
Maňuch, J., Patterson, M., Gupta, A.: On the Generalised Character Compatibility Problem for Non-branching Character Trees. In: Ngo, H.Q. (ed.) COCOON 2009. LNCS, vol. 5609, pp. 268–276. Springer, Heidelberg (2009)
McMorris, F., Warnow, T., Wimer, T.: Triangulating vertex colored graphs. SIAM J. Discrete Mathematics 7(2), 296–306 (1994)
Meidanis, J., Porto, O., Telles, G.P.: On the consecutive ones property. Discrete Applied Mathematics 155, 788–805 (2007)
Opatrny, J.: Total ordering problem. SIAM J. Computing 8(1), 111–114 (1979)
Pe’er, I., Pupko, T., Shamir, R., Sharan, R.: Incomplete directed perfect phylogeny. SIAM J. Computing 33, 590–607 (2004)
Steel, M.: The complexity of reconstructing trees from qualitative characters and subtrees. J. Classification 9, 91–116 (1992)
Trowsdale, J.: Genomic structure and function in the MHC. Trends in Genetics 9, 117–122 (1993)
Warnow, T.: Tree compatibility and inferring evolutionary history. J. Algorithms 16, 388–407 (1994)
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Maňuch, J., Patterson, M., Gupta, A. (2011). Towards a Characterisation of the Generalised Cladistic Character Compatibility Problem for Non-branching Character Trees. In: Chen, J., Wang, J., Zelikovsky, A. (eds) Bioinformatics Research and Applications. ISBRA 2011. Lecture Notes in Computer Science(), vol 6674. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21260-4_41
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