Computing the rooted triplet distance between galled trees by counting triangles

Authors:
Jesper Jansson;Andrzej Lingas
Affiliations:
Laboratory of Mathematical Bioinformatics, Institute for Chemical Research, Kyoto University, Uji, Kyoto, Japan;Department of Computer Science, Lund University, Lund, Sweden
Venue:
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Year:
2012

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Abstract

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(n2.688) time. Our upper bound is obtained by reducing the problem of computing the rooted triplet distance 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 related results that may be of independent interest.