Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Reconstructing reticulate evolution in species: theory and practice
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Algorithms for combining rooted triplets into a galled phylogenetic network
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
An efficient exact algorithm for the minimum ultrametric tree problem
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
The maximum agreement of two nested phylogenetic networks
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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
Constructing a smallest refining galled phylogenetic network
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
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Given a distance matrix M that specifies the pairwise evolutionary distances between n species, the phylogenetic tree reconstruction problem asks for an edge-weighted phylogenetic tree that satisfies M, if one exists. We study some extensions of this problem to rooted phylogenetic networks. Our main result is an O(n2 log n)-time algorithm for determining whether there is an ultrametric galled network that satisfies M, and if so, constructing one. In fact, if such an ultrametric galled network exists, our algorithm is guaranteed to construct one containing the minimum possible number of nodes with more than one parent (hybrid nodes). We also prove that finding a largest possible submatrix M′ of M such that there exists an ultrametric galled network that satisfies M′ is NP-hard. Furthermore, we show that given an incomplete distance matrix (i.e., where some matrix entries are missing), it is also NP-hard to determine whether there exists an ultrametric galled network which satisfies it.