@MISC{_level-kphylogenetic, author = {}, title = {LEVEL-K PHYLOGENETIC NETWORK CAN BE CONSTRUCTED FROM A DENSE TRIPLET SET IN POLYNOMIAL TIME THU-HIEN TO AND MICHEL HABIB}, year = {} }

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Abstract

Abstract. Given a dense triplet set T, there arise two interesting questions [7]: Does there exists any phylogenetic network consistent with T? And if so, can we find an effective algorithm to construct one? For cases of networks of levels k = 0 or 1 or 2, these questions were answered in [1, 6, 7, 8, 10] with effective polynomial algorithms. For higher levels k, partial answers were recently obtained in [11] with an O(|T | k+1) time algorithm for simple networks. In this paper we give a complete answer to the general case, solving a problem of [7]. The main idea is to use a special property of SN-sets in a level-k network. As a consequence, we can also find the level-k network with the minimum number of reticulations in polynomial time. hal-00352360, version 1- 12 Jan 2009 1.