Experimental analysis of a new algorithm for partial haplotype completion
International Journal of Bioinformatics Research and Applications
The approximability of MAX CSP with fixed-value constraints
Journal of the ACM (JACM)
The Undirected Incomplete Perfect Phylogeny Problem
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Influence of Tree Topology Restrictions on the Complexity of Haplotyping with Missing Data
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
ISBRA'11 Proceedings of the 7th international conference on Bioinformatics research and applications
FlipCut supertrees: towards matrix representation accuracy in polynomial time
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Efficiently solvable perfect phylogeny problems on binary and k-state data with missing values
WABI'11 Proceedings of the 11th international conference on Algorithms in bioinformatics
Experimental analysis of a new algorithm for partial haplotype completion
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
Influence of tree topology restrictions on the complexity of haplotyping with missing data
Theoretical Computer Science
Efficient enumeration of the directed binary perfect phylogenies from incomplete data
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
The binary perfect phylogeny with persistent characters
Theoretical Computer Science
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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Perfect phylogeny is one of the fundamental models for studying evolution. We investigate the following variant of the model: The input is a species-characters matrix. The characters are binary and directed; i.e., a species can only gain characters. The difference from standard perfect phylogeny is that for some species the states of some characters are unknown. The question is whether one can complete the missing states in a way that admits a perfect phylogeny. The problem arises in classical phylogenetic studies, when some states are missing or undetermined. Quite recently, studies that infer phylogenies using inserted repeat elements in DNA gave rise to the same problem. Extant solutions for it take time O(n2m) for n species and m characters. We provide a graph theoretic formulation of the problem as a graph sandwich problem, and give near-optimal $\tilde{O}(nm)$-time algorithms for the problem. We also study the problem of finding a single, general solution tree, from which any other solution can be obtained by node splitting. We provide an algorithm to construct such a tree, or determine that none exists.