Abstract. In this paper, we introduce new algorithms for selecting taxon (leaf) samples from large phylogenetic trees, uniformly at random, under certain biologically relevant constraints on the taxa. All the algorithms run in polynomial time and have been implemented. The algorithms have direct applications to the evaluation of phylogenetic tree and supertree construction methods using biologically curated data. We also relate one of the sampling problems to the well-known clique problem on undirected graphs. From this, we obtain an interesting new class of graphs for which many open problems exist.

BackgroundThe neighbor-joining method by Saitou and Nei is a widely used method for constructing phylogenetic trees. The formulation of the method gives rise to a canonical Θ(n3) algorithm upon which all existing implementations are based.ResultsIn this paper we present techniques for speeding up the canonical neighbor-joining method. Our algorithms construct the same phylogenetic trees as the canonical neighbor-joining method. The best-case running time of our algorithms are O(n2) but the worst-case remains O(n3). We empirically evaluate the performance of our algoritms on distance matrices obtained from the Pfam collection of alignments. The experiments indicate that the running time of our algorithms evolve as Θ(n2) on the examined instance collection. We also compare the running time with that of the QuickTree tool, a widely used efficient implementation of the canonical neighbor-joining method.ConclusionThe experiments show that our algorithms also yield a significant speed-up, already for medium sized instances.

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