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arXiv · 1701.02844

Selecting optimal minimum spanning trees that share a topological correspondence with phylogenetic trees

Prabhav Kalaghatgi·Thomas Lengauer
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Abstract

Choi et. al (2011) introduced a minimum spanning tree (MST)-based method called CLGrouping, for constructing tree-structured probabilistic graphical models, a statistical framework that is commonly used for inferring phylogenetic trees. While CLGrouping works correctly if there is a unique MST, we observe an indeterminacy in the method in the case that there are multiple MSTs. In this work we remove this indeterminacy by introducing so-called vertex-ranked MSTs. We note that the effectiveness of CLGrouping is inversely related to the number of leaves in the MST. This motivates the problem of finding a vertex-ranked MST with the minimum number of leaves (MLVRMST). We provide a polynomial time algorithm for the MLVRMST problem, and prove its correctness for graphs whose edges are weighted with tree-additive distances.

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Prabhav Kalaghatgi, Thomas Lengauer. 2017-01-11. Selecting optimal minimum spanning trees that share a topological correspondence with phylogenetic trees. https://arxiv.org/abs/1701.02844

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