




Charles Choy,
Jesper Jansson,
Kunihiko Sadakane and
WingKin Sung. Computing the maximum agreement of phylogenetic networks. In TCS, Vol. 335(1):93107, 2005. Keywords: dynamic programming, FPT, level k phylogenetic network, MASN, NP complete, phylogenetic network, phylogeny. Note: http://www.df.lth.se/~jj/Publications/masn8_TCS2005.pdf.
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"We introduce the maximum agreement phylogenetic subnetwork problem (MASN) for finding branching structure shared by a set of phylogenetic networks. We prove that the problem is NPhard even if restricted to three phylogenetic networks and give an O(n2)time algorithm for the special case of two level1 phylogenetic networks, where n is the number of leaves in the input networks and where N is called a levelf phylogenetic network if every biconnected component in the underlying undirected graph induces a subgraph of N containing at most f nodes with indegree 2. We also show how to extend our technique to yield a polynomialtime algorithm for any two levelf phylogenetic networks N1,N2 satisfying f=O(logn); more precisely, its running time is O(V(N1)·V(N2)·2f1+f2), where V(Ni) and fi denote the set of nodes in Ni and the level of Ni, respectively, for i∈{1,2}. © 2005 Elsevier B.V. All rights reserved."






Charles Choy,
Jesper Jansson,
Kunihiko Sadakane and
WingKin Sung. Computing the maximum agreement of phylogenetic networks. In Proceedings of Computing: the Tenth Australasian Theory Symposium (CATS'04), Vol. 91:134147 of Electronic Notes in Theoretical Computer Science, 2004. Keywords: dynamic programming, FPT, level k phylogenetic network, MASN, NP complete, phylogenetic network, phylogeny. Note: http://www.df.lth.se/~jj/Publications/masn6_CATS2004.pdf.
Toggle abstract
"We introduce the maximum agreement phylogenetic subnetwork problem (MASN) of finding a branching structure shared by a set of phylogenetic networks. We prove that the problem is NPhard even if restricted to three phylogenetic networks and give an O(n2)time algorithm for the special case of two level1 phylogenetic networks, where n is the number of leaves in the input networks and where N is called a levelf phylogenetic network if every biconnected component in the underlying undirected graph contains at most f nodes having indegree 2 in N. Our algorithm can be extended to yield a polynomialtime algorithm for two levelf phylogenetic networks N 1,N2 for any f which is upperbounded by a constant; more precisely, its running time is O(V(N1)·V(N 2)·4f), where V(Ni) denotes the set of nodes of Ni. © 2004 Published by Elsevier B.V."



