Introduction to algorithms
Kaikoura tree theorems: computing the maximum agreement subtree
Information Processing Letters
On the agreement of many trees
Information Processing Letters
Maximum Agreement Subtree in a Set of Evolutionary Trees: Metrics and Efficient Algorithms
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
An O(nlog n) Algorithm for the Maximum Agreement Subtree Problem for Binary Trees
SIAM Journal on Computing
NeighborNet: An Agglomerative Method for the Construction of Planar Phylogenetic Networks
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Efficient Reconstruction of Phylogenetic Networks with Constrained Recombination
CSB '03 Proceedings of the IEEE Computer Society Conference on Bioinformatics
Reconstructing reticulate evolution in species: theory and practice
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Unicyclic Networks: Compatibility and Enumeration
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Inferring Pedigree Graphs from Genetic Distances
IEICE - Transactions on Information and Systems
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Fast algorithms for computing the tripartition-based distance between phylogenetic networks
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Reconstructing an ultrametric galled phylogenetic network from a distance matrix
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
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Given a set ${\mathcal N}$ of phylogenetic networks, the maximum agreement phylogenetic subnetwork problem (MASN) asks for a subnetwork contained in every $N_{i} \in {\mathcal N}$ with as many leaves as possible MASN can be used to identify shared branching structure among phylogenetic networks or to measure their similarity In this paper, we prove that the general case of MASN is NP-hard already for two phylogenetic networks, but that the problem can be solved efficiently if the two given phylogenetic networks exhibit a nested structure We first show that the total number of nodes |V(N)| in any nested phylogenetic network N with n leaves and nesting depth d is O(n (d +1)) We then describe an algorithm for testing if a given phylogenetic network is nested, and if so, determining its nesting depth in O(|V(N)| · (d + 1)) time Next, we present a polynomial-time algorithm for MASN for two nested phylogenetic networks N1, N2 Its running time is O(|V(N1)| · |V(N2)| · (d1 + 1) · (d2 + 1)), where d1 and d2 denote the nesting depths of N1 and N2, respectively In contrast, the previously fastest algorithm for this problem runs in O(|V(N1)| · |V(N2)| · 4f) time, where f≥max{d1,d2}.