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Accurate reconstruction of phylogenies remains a key challenge inevolutionary biology. Most biologically plausible formulations of the problemare formally NP-hard, with no known efficient solution. The standard inpractice are fast heuristic methods that are empirically known to work verywell in general, but can yield results arbitrarily far from optimal. Practicalexact methods, which yield exponential worst-case running times but generallymuch better times in practice, provide an important alternative. We reportprogress in this direction by introducing a provably optimal method for theweighted multi-state maximum parsimony phylogeny problem. The method is basedon generalizing the notion of the Buneman graph, a construction key toefficient exact methods for binary sequences, so as to apply to sequences witharbitrary finite numbers of states with arbitrary state transition weights. Weimplement an integer linear programming (ILP) method for the multi-stateproblem using this generalized Buneman graph and demonstrate that the resultingmethod is able to solve data sets that are intractable by prior exact methodsin run times comparable with popular heuristics. Our work provides the firstmethod for provably optimal maximum parsimony phylogeny inference that ispractical for multi-state data sets of more than a few characters.

Generalized Buneman pruning for inferring the most parsimonious multi-state phylogeny