





Lavanya Kannan and
Ward C Wheeler. Exactly Computing the Parsimony Scores on Phylogenetic Networks Using Dynamic Programming. In JCB, Vol. 21(4):303319, 2014. Keywords: explicit network, exponential algorithm, from network, from sequences, parsimony, phylogenetic network, phylogeny, reconstruction.
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"Scoring a given phylogenetic network is the first step that is required in searching for the best evolutionary framework for a given dataset. Using the principle of maximum parsimony, we can score phylogenetic networks based on the minimum number of state changes across a subset of edges of the network for each character that are required for a given set of characters to realize the input states at the leaves of the networks. Two such subsets of edges of networks are interesting in light of studying evolutionary histories of datasets: (i) the set of all edges of the network, and (ii) the set of all edges of a spanning tree that minimizes the score. The problems of finding the parsimony scores under these two criteria define slightly different mathematical problems that are both NPhard. In this article, we show that both problems, with scores generalized to adding substitution costs between states on the endpoints of the edges, can be solved exactly using dynamic programming. We show that our algorithms require O(mpk) storage at each vertex (per character), where k is the number of states the character can take, p is the number of reticulate vertices in the network, m = k for the problem with edge set (i), and m = 2 for the problem with edge set (ii). This establishes an O(nmpk2) algorithm for both the problems (n is the number of leaves in the network), which are extensions of Sankoff's algorithm for finding the parsimony scores for phylogenetic trees. We will discuss improvements in the complexities and show that for phylogenetic networks whose underlying undirected graphs have disjoint cycles, the storage at each vertex can be reduced to O(mk), thus making the algorithm polynomial for this class of networks. We will present some properties of the two approaches and guidance on choosing between the criteria, as well as traverse through the network space using either of the definitions. We show that our methodology provides an effective means to study a wide variety of datasets. © Copyright 2014, Mary Ann Liebert, Inc. 2014."





Benjamin Albrecht. Computing all hybridization networks for multiple binary phylogenetic input trees. In BMCB, Vol. 16(236):115, 2015. Keywords: agreement forest, explicit network, exponential algorithm, FPT, from rooted trees, phylogenetic network, phylogeny, Program Hybroscale, Program PIRN, reconstruction. Note: http://dx.doi.org/10.1186/s1285901506607.






Ernst Althaus and
Rouven Naujoks. Reconstructing Phylogenetic Networks with One Recombination. In Proceedings of the seventh International Workshop on Experimental Algorithms (WEA'08), Vol. 5038:275288 of LNCS, springer, 2008. Keywords: enumeration, explicit network, exponential algorithm, from sequences, generation, parsimony, phylogenetic network, phylogeny, reconstruction, unicyclic network. Note: http://dx.doi.org/10.1007/9783540685524_21.
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"In this paper we propose a new method for reconstructing phylogenetic networks under the assumption that recombination events have occurred rarely. For a fixed number of recombinations, we give a generalization of the maximum parsimony criterion. Furthermore, we describe an exact algorithm for one recombination event and show that in this case our method is not only able to identify the recombined sequence but also to reliably reconstruct the complete evolutionary history. © 2008 SpringerVerlag Berlin Heidelberg."



Katharina Huber,
Vincent Moulton,
Andreas Spillner,
Sabine Storandt and
Radoslaw Suchecki. Computing a consensus of multilabeled trees. In ALENEX12, Pages 8492, 2012. Keywords: duplication, explicit network, exponential algorithm, phylogenetic network, phylogeny. Note: http://siam.omnibooksonline.com/2012ALENEX/data/papers/020.pdf.
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In this paper we consider two challenging problems that arise in the context of computing a consensus of a collection of multilabeled trees, namely (1) selecting a compatible collection of clusters on a multiset from an ordered list of such clusters and (2) optimally refining high degree vertices in a multilabeled tree. Forming such a consensus is part of an approach to reconstruct the evolutionary history of a set of species for which events such as genome duplication and hybridization have occurred in the past. We present exact algorithms for solving (1) and (2) that have an exponential runtime in the worst case. To give some impression of their performance in practice, we apply them to simulated input and to a real biological data set highlighting the impact of several structural properties of the input on the performance.



Yufeng Wu. An Algorithm for Constructing Parsimonious Hybridization Networks with Multiple Phylogenetic Trees. In RECOMB13, Vol. 7821:291303 of LNCS, springer, 2013. Keywords: explicit network, exponential algorithm, from rooted trees, phylogenetic network, phylogeny, Program PIRN, reconstruction. Note: http://www.engr.uconn.edu/~ywu/Papers/ExactNetRecomb2013.pdf.
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"Phylogenetic network is a model for reticulate evolution. Hybridization network is one type of phylogenetic network for a set of discordant gene trees, and "displays" each gene tree. A central computational problem on hybridization networks is: given a set of gene trees, reconstruct the minimum (i.e. most parsimonious) hybridization network that displays each given gene tree. This problem is known to be NPhard, and existing approaches for this problem are either heuristics or make simplifying assumptions (e.g. work with only two input trees or assume some topological properties). In this paper, we develop an exact algorithm (called PIRNC ) for inferring the minimum hybridization networks from multiple gene trees. The PIRNC algorithm does not rely on structural assumptions. To the best of our knowledge, PIRN C is the first exact algorithm for this formulation. When the number of reticulation events is relatively small (say four or fewer), PIRNC runs reasonably efficient even for moderately large datasets. For building more complex networks, we also develop a heuristic version of PIRNC called PIRNCH. Simulation shows that PIRNCH usually produces networks with fewer reticulation events than those by an existing method. © 2013 SpringerVerlag."





Bingxin Lu,
Louxin Zhang and
Hon Wai Leong. A program to compute the soft RobinsonFoulds distance between phylogenetic networks. In APBC17, Vol. 18(Suppl. 2):111 of BMC Genomics, 2017. Keywords: cluster containment, distance between networks, explicit network, exponential algorithm, from network, phylogenetic network, phylogeny, Program iceluPhyloNetwork. Note: http://dx.doi.org/10.1186/s1286401735005.






Leo van Iersel. Algorithms, Haplotypes and Phylogenetic Networks. PhD thesis, Eindhoven University of Technology, The Netherlands, 2009. Keywords: evaluation, explicit network, exponential algorithm, FPT, from triplets, galled tree, level k phylogenetic network, mu distance, phylogenetic network, phylogeny, polynomial, Program Level2, Program Marlon, Program Simplistic, Program T REX, reconstruction. Note: http://www.win.tue.nl/~liersel/thesis_vaniersel_viewing.pdf.





