Hypothesis testing in perfect phylogeny for a bounded number of characters

Abstract

We introduce the hypothesis testing problem (HTP). In HTP the input is a family of species F and a hypothesis, i.e., a tree where the leaves are labeled with species from some subfamily of F. The problem is to decide whether there is a perfect phylogeny for F which agrees with the hypothesis. We show that HTP can be solved in O(m ² r ^m|F|(|F|+mr)) time, where m is the number of characters and r is the maximum number of states on any character. We obtain an O(m ³ r ^m+1 + |F|m ²) algorithm for the perfect phylogeny problem (PPP), as well. The fastest previously known algorithm for PPP, with fixed m, has running time O(m ^m+1 r ^m+1 + |F|m ²) [10]. We also consider several variations of HTP which we either show to be solvable in polynomial time or NP-complete.

Supported by grants from NFR and TFR.