Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Fixed topology alignment with recombination
Discrete Applied Mathematics - Special volume on combinatorial molecular biology
Computing the maximum agreement of phylogenetic networks
Theoretical Computer Science - Pattern discovery in the post genome
Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network
SIAM Journal on Computing
Metrics for Phylogenetic Networks II: Nodal and Triplets Metrics
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Finding heaviest H-subgraphs in real weighted graphs, with applications
ACM Transactions on Algorithms (TALG)
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Phylogenetic Networks: Concepts, Algorithms and Applications
Phylogenetic Networks: Concepts, Algorithms and Applications
Comparing and aggregating partially resolved trees
Theoretical Computer Science
Multiplying matrices faster than coppersmith-winograd
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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We consider a generalization of the rooted triplet distance between two phylogenetic trees to two phylogenetic networks. We show that if each of the two given phylogenetic networks is a so-called galled tree with n leaves then the rooted triplet distance can be computed in o(n^2^.^6^8^7) time. Our upper bound is obtained by reducing the problem of computing the rooted triplet distance between two galled trees to that of counting monochromatic and almost-monochromatic triangles in an undirected, edge-colored graph. To count different types of colored triangles in a graph efficiently, we extend an existing technique based on matrix multiplication and obtain several new algorithmic results that may be of independent interest: (i) the number of triangles in a connected, undirected, uncolored graph with m edges can be computed in o(m^1^.^4^0^8) time; (ii) if G is a connected, undirected, edge-colored graph with n vertices and C is a subset of the set of edge colors then the number of monochromatic triangles of G with colors in C can be computed in o(n^2^.^6^8^7) time; and (iii) if G is a connected, undirected, edge-colored graph with n vertices and R is a binary relation on the colors that is computable in O(1) time then the number of R-chromatic triangles in G can be computed in o(n^2^.^6^8^7) time.