Structural parsimony: Reductions in sequence space

Computational phylogenetics has historically neglected strict theoretical approaches that exploit the mathematical models beneath which it abstracts away the nuances of evolution. In particular, parsimony is conceptually simple and amenable to rigorous treatment, and has a clear analogue in graph theory, the Steiner tree. We present and refine the notion of sequence space as the soil from which all graph-theoretical methods arise, studying its structural properties and complexity with an eye on maximum parsimony. We therefrom introduce a basic set of very efficient implicit reductions that discard information with a fixed effect on the optimality of the solution, and show how it can be applied to large, real datasets.