Common Contracts
1 similar Maximum Agreement contracts
The Maximum Agreement of Two Nested Phylogenetic NetworksMaximum Agreement • November 9th, 2004
Abstract. Given a set of phylogenetic networks, the maximum agree- ment phylogenetic subnetwork problem (MASN) asks for a subnetwork contained in every Ni with as many leaves as possible. MASN can be used to identify shared branching structure among phylogenetic networks or to measure their similarity. In this paper, we prove that the general case of MASN is NP-hard already for two phylogenetic networks, but that the problem can be solved efficiently if the two given phylogenetic networks exhibit a nested structure. We first show that the total number of nodes V (N ) in any nested phylogenetic network N with n leaves and nesting depth d is O(n(d + 1)). We then describe an algorithm for testing if a given phylogenetic network is nested, and if so, determin- ing its nesting depth in O( V (N ) (d + 1)) time. Next, we present a polynomial-time algorithm for MASN for two nested phylogenetic net- works N1, N2. Its running time is O( V (N1) V (N2) (d1 + 1) (d2 + 1)), where d1 and d2 denote the n
