On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
On the complexity of comparing evolutionary trees
Discrete Applied Mathematics - Special volume on computational molecular biology
Computing the minimum number of hybridization events for a consistent evolutionary history
Discrete Applied Mathematics
Computing the Hybridization Number of Two Phylogenetic Trees Is Fixed-Parameter Tractable
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Bioinformatics
Fast FPT algorithms for computing rooted agreement forests: theory and experiments
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
Fast computation of the exact hybridization number of two phylogenetic trees
ISBRA'10 Proceedings of the 6th international conference on Bioinformatics Research and Applications
A practical approximation algorithm for solving massive instances of hybridization number
WABI'12 Proceedings of the 12th international conference on Algorithms in Bioinformatics
An algorithm for constructing parsimonious hybridization networks with multiple phylogenetic trees
RECOMB'13 Proceedings of the 17th international conference on Research in Computational Molecular Biology
A quadratic kernel for computing the hybridization number of multiple trees
Information Processing Letters
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A reticulate network N of multiple phylogenetic trees may have nodes with two or more parents (called reticulation nodes). There are two ways to define the reticulation number of N. One way is to define it as the number of reticulation nodes in N in this case, a reticulate network with the smallest reticulation number is called an optimal type-I reticulate network of the trees. The better way is to define it as the total number of parents of reticulation nodes in N minus the number of reticulation nodes in N ; in this case, a reticulate network with the smallest reticulation number is called an optimal type-II reticulate network of the trees. In this paper, we first present a fast fixed-parameter algorithm for constructing one or all optimal type-I reticulate networks of multiple phylogenetic trees. We then use the algorithm together with other ideas to obtain an algorithm for estimating a lower bound on the reticulation number of an optimal type-II reticulate network of the input trees. To our knowledge, these are the first fixed-parameter algorithms for the problems. We have implemented the algorithms in ANSI C, obtaining programs CMPT and MaafB. Our experimental data show that CMPT can construct optimal type-I reticulate networks rapidly and MaafB can compute better lower bounds for optimal type-II reticulate networks within shorter time than the previously best program PIRN designed by Wu.