Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Reconciliation problems for duplication, loss and horizontal gene transfer
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Reconstructing reticulate evolution in species: theory and practice
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Simultaneous identification of duplications and lateral transfers
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Phylogenetic Networks: Modeling, Reconstructibility, and Accuracy
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Reconstructing Phylogenetic Networks Using Maximum Parsimony
CSB '05 Proceedings of the 2005 IEEE Computational Systems Bioinformatics Conference
Maximum likelihood of phylogenetic networks
Bioinformatics
Reconstructing Recombination Network from Sequence Data: The Small Parsimony Problem
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A fundamental decomposition theory for phylogenetic networks and incompatible characters
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Reconstruction of reticulate networks from gene trees
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Constructing a smallest refining galled phylogenetic network
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Improved recombination lower bounds for haplotype data
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Detecting highways of horizontal gene transfer
RECOMB-CG'10 Proceedings of the 2010 international conference on Comparative genomics
RECOMB'12 Proceedings of the 16th Annual international conference on Research in Computational Molecular Biology
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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.