The Complexity of Inferring a Minimally Resolved Phylogenetic Supertree

Abstract. A recursive algorithm by Aho, Sagiv, Szymanski, and Ullman [1] forms the basis for many modern rooted supertree methods employed in Phylogenetics. However, as observed by Bryant [4], the tree output by the algorithm of Aho et al. is not always minimal; there may exist other trees which contain fewer nodes yet are still consistent with the input. In this paper, we prove strong polynomial-time inapproximability results for the problem of inferring a minimally resolved supertree from a given consistent set of rooted triplets (MinRS). We also present an exponential-time algorithm for solving MinRS exactly which is based on tree separators. It runs in 2O(n log k) time when every node is required to have at most k children which are internal nodes and where n is the cardinality of the leaf label set of the input trees.

• Type: Journal
• Year: 2010
• Where: WABI
• Authors: Jesper Jansson, Richard S. Lemence, Andrzej Lingas
• Keywords: Algorithm, Bioinformatics, Modern Rooted Supertree, Strong Polynomial-time Inapproximability, WABI 2010