@online{Kalaghatgi2017,
TITLE = {Selecting Optimal Minimum Spanning Trees that Share a Topological Correspondence with Phylogenetic Trees},
AUTHOR = {Kalaghatgi, Prabhav and Lengauer, Thomas},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1701.02844},
EPRINT = {1701.02844},
EPRINTTYPE = {arXiv},
YEAR = {2017},
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.},
}