A fast algorithm for reordering sparse matrices for parallel factorization
SIAM Journal on Scientific and Statistical Computing
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Tree compatibility and inferring evolutionary history
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Perfect phylogeny and haplotype assignment
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Incomplete Directed Perfect Phylogeny
SIAM Journal on Computing
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
The Undirected Incomplete Perfect Phylogeny Problem
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Exact Computation of Coalescent Likelihood under the Infinite Sites Model
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Reducing problems in unrooted tree compatibility to restricted triangulations of intersection graphs
WABI'12 Proceedings of the 12th international conference on Algorithms in Bioinformatics
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The perfect phylogeny problem is of central importance to both evolutionary biology and population genetics. Missing values are a common occurrence in both sequence and genotype data. In their presence, the problem of finding a perfect phylogeny is NP-hard, even for binary characters [24]. We extend the utility of the perfect phylogeny by introducing new efficient algorithms for broad classes of binary and multi-state data with missing values. Specifically, we address the rich data hypothesis introduced by Halperin and Karp [11] for the binary perfect phylogeny problem with missing data. We give an efficient algorithm for enumerating phylogenies compatible with characters satisfying the rich data hypothesis. This algorithm is useful for computing the probability of data with missing values under the coalescent model. In addition, we use the partition intersection (PI) graph and chordal graph theory to generalize the rich data hypothesis to multi-state characters with missing values. For a bounded number of states, k, we provide a fixed parameter tractable algorithm for the k-state perfect phylogeny problem with missing data. Our approach reduces missing data problems to problems on complete data. Finally, we characterize a commonly observed condition, an m-clique in the PI graph, under which a perfect phylogeny can be found efficiently for binary characters with missing values. We evaluate our results with extensive empirical analysis using two biologically motivated generative models of character data.