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A new lineartime heuristic algorithm for computing the the parsimony score of phylogenetic networks: theoretical bounds and empirical performance
 ISBRA 2007. LNCS (LNBI
, 2007
"... Phylogenies play a major role in representing the interrelationships among biological entities. Many methods for reconstructing and studying such phylogenies have been proposed, almost all of which assume that the underlying history of a given set of species can be represented by a binary tree. Alt ..."
Abstract

Cited by 6 (3 self)
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Phylogenies play a major role in representing the interrelationships among biological entities. Many methods for reconstructing and studying such phylogenies have been proposed, almost all of which assume that the underlying history of a given set of species can be represented by a binary tree. Although many biological processes can be effectively modeled and summarized in this fashion, others cannot: recombination, hybrid speciation, and horizontal gene transfer result in networks, rather than trees, of relationships. In a series of papers, we have extended the maximum parsimony (MP) criterion to phylogenetic networks, demonstrated its appropriateness, and established the intractability of the problem of scoring the parsimony of a phylogenetic network. In this work we show the hardness of approximation for the general case of the problem, devise a very fast (lineartime) heuristic algorithm for it, and implement it on simulated as well as biological data.
Parsimony score of phylogenetic networks: Hardness results and a lineartime heuristic
 IEEE/ACM TRANS. COMPUT. BIOLOGY BIOINFORM
, 2009
"... Phylogenies—the evolutionary histories of groups of organisms—play a major role in representing the interrelationships among biological entities. Many methods for reconstructing and studying such phylogenies have been proposed, almost all of which assume that the underlying history of a given set o ..."
Abstract

Cited by 5 (2 self)
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Phylogenies—the evolutionary histories of groups of organisms—play a major role in representing the interrelationships among biological entities. Many methods for reconstructing and studying such phylogenies have been proposed, almost all of which assume that the underlying history of a given set of species can be represented by a binary tree. Although many biological processes can be effectively modeled and summarized in this fashion, others cannot: recombination, hybrid speciation, and horizontal gene transfer result in networks of relationships rather than trees of relationships. In previous works, we formulated a maximum parsimony (MP) criterion for reconstructing and evaluating phylogenetic networks, and demonstrated its quality on biological as well as synthetic data sets. In this paper, we provide further theoretical results as well as a very fast heuristic algorithm for the MP criterion of phylogenetic networks. In particular, we provide a novel combinatorial definition of phylogenetic networks in terms of “forbidden cycles, ” and provide detailed hardness and hardness of approximation proofs for the “small ” MP problem. We demonstrate the performance of our heuristic in terms of time and accuracy on both biological and synthetic data sets. Finally, we explain the difference between our model and a similar one formulated by Nguyen et al., and describe the implications of this difference on the hardness and approximation results.
COUNTING TREES IN A PHYLOGENETIC NETWORK IS #PCOMPLETE ∗
"... Abstract. Answering a problem posed by Nakhleh, we prove that counting the number of phylogenetic trees inferred by a (binary) phylogenetic network is #Pcomplete. An immediate consequence of this result is that counting the number of phylogenetic trees commonly inferred by two (binary) phylogenetic ..."
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Abstract. Answering a problem posed by Nakhleh, we prove that counting the number of phylogenetic trees inferred by a (binary) phylogenetic network is #Pcomplete. An immediate consequence of this result is that counting the number of phylogenetic trees commonly inferred by two (binary) phylogenetic networks is also #Pcomplete. Key words. Phylogenetic trees, phylogenetic networks, #Pcomplete 1. Introduction. A