
Tetsuo Asano,
Jesper Jansson,
Kunihiko Sadakane,
Ryuhei Uehara and
Gabriel Valiente. Faster computation of the Robinson–Foulds distance between phylogenetic networks. In Information Sciences, Vol. 197:7790, 2012. Keywords: distance between networks, explicit network, level k phylogenetic network, phylogenetic network, polynomial, spread.
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"The RobinsonFoulds distance, a widely used metric for comparing phylogenetic trees, has recently been generalized to phylogenetic networks. Given two phylogenetic networks N 1, N 2 with n leaf labels and at most m nodes and e edges each, the RobinsonFoulds distance measures the number of clusters of descendant leaves not shared by N 1 and N 2. The fastest known algorithm for computing the RobinsonFoulds distance between N 1 and N 2 runs in O(me) time. In this paper, we improve the time complexity to O(ne/log n) for general phylogenetic networks and O(nm/log n) for general phylogenetic networks with bounded degree (assuming the word RAM model with a word length of ⌈logn⌉ bits), and to optimal O(m) time for leafouterplanar networks as well as optimal O(n) time for level1 phylogenetic networks (that is, galledtrees). We also introduce the natural concept of the minimum spread of a phylogenetic network and show how the running time of our new algorithm depends on this parameter. As an example, we prove that the minimum spread of a levelk network is at most k + 1, which implies that for one level1 and one levelk phylogenetic network, our algorithm runs in O((k + 1)e) time. © 2012 Elsevier Inc. All rights reserved."



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."





Hoa Vu,
Francis Chin,
WingKai Hon,
Henry Leung,
Kunihiko Sadakane,
WingKin Sung and
SiuMing Yiu. Reconstructing kReticulated Phylogenetic Network from a Set of Gene Trees. In ISBRA13, Vol. 7875:112124 of LNCS, springer, 2013. Keywords: from rooted trees, kreticulated, phylogenetic network, phylogeny, polynomial, Program ARTNET, Program CMPT, reconstruction. Note: http://grid.cs.gsu.edu/~xguo9/publications/2013_Cloud%20computing%20for%20de%20novo%20metagenomic%20sequence%20assembly.pdf#page=123.
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"The time complexity of existing algorithms for reconstructing a levelx phylogenetic network increases exponentially in x. In this paper, we propose a new classification of phylogenetic networks called kreticulated network. A kreticulated network can model all levelk networks and some levelx networks with x > k. We design algorithms for reconstructing kreticulated network (k = 1 or 2) with minimum number of hybrid nodes from a set of m binary trees, each with n leaves in O(mn 2) time. The implication is that some levelx networks with x > k can now be reconstructed in a faster way. We implemented our algorithm (ARTNET) and compared it with CMPT. We show that ARTNET outperforms CMPT in terms of running time and accuracy. We also consider the case when there does not exist a 2reticulated network for the input trees. We present an algorithm computing a maximum subset of the species set so that a new set of subtrees can be combined into a 2reticulated network. © 2013 SpringerVerlag."



Tetsuo Asano,
Jesper Jansson,
Kunihiko Sadakane,
Ryuhei Uehara and
Gabriel Valiente. Faster Computation of the RobinsonFoulds Distance between Phylogenetic Networks. In CPM10, Vol. 6129:190201 of LNCS, springer, 2010. Keywords: distance between networks, explicit network, level k phylogenetic network, phylogenetic network, polynomial, spread. Note: http://hdl.handle.net/10119/9859, slides available at http://cs.nyu.edu/parida/CPM2010/MainPage_files/18.pdf.
Toggle abstract
"The RobinsonFoulds distance, which is the most widely used metric for comparing phylogenetic trees, has recently been generalized to phylogenetic networks. Given two networks N1,N2 with n leaves, m nodes, and e edges, the RobinsonFoulds distance measures the number of clusters of descendant leaves that are not shared by N1 and N2. The fastest known algorithm for computing the RobinsonFoulds distance between those networks runs in O(m(m + e)) time. In this paper, we improve the time complexity to O(n(m+ e)/ log n) for general networks and O(nm/log n) for general networks with bounded degree, and to optimal O(m + e) time for planar phylogenetic networks and boundedlevel phylogenetic networks.We also introduce the natural concept of the minimum spread of a phylogenetic network and show how the running time of our new algorithm depends on this parameter. As an example, we prove that the minimum spread of a levelk phylogenetic network is at most k + 1, which implies that for two levelk phylogenetic networks, our algorithm runs in O((k + 1)(m + e)) time. © SpringerVerlag Berlin Heidelberg 2010."



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."



