%0 Journal Article
%T The Ultrametric Constraint and its Application to Phylogenetics
%A Neil C. A. Moore
%A Patrick Prosser
%J Computer Science
%D 2014
%I arXiv
%R 10.1613/jair.2580
%X A phylogenetic tree shows the evolutionary relationships among species. Internal nodes of the tree represent speciation events and leaf nodes correspond to species. A goal of phylogenetics is to combine such trees into larger trees, called supertrees, whilst respecting the relationships in the original trees. A rooted tree exhibits an ultrametric property; that is, for any three leaves of the tree it must be that one pair has a deeper most recent common ancestor than the other pairs, or that all three have the same most recent common ancestor. This inspires a constraint programming encoding for rooted trees. We present an efficient constraint that enforces the ultrametric property over a symmetric array of constrained integer variables, with the inevitable property that the lower bounds of any three variables are mutually supportive. We show that this allows an efficient constraint-based solution to the supertree construction problem. We demonstrate that the versatility of constraint programming can be exploited to allow solutions to variants of the supertree construction problem.
%U http://arxiv.org/abs/1401.3438v1