The kernel of maximum agreement subtrees

Authors:
Krister M. Swenson;Eric Chen;Nicholas D. Pattengale;David Sankoff
Affiliations:
Department of Mathematics and Statistics, University of Ottawa, Ontario, Canada and LaCIM, UQAM, Montréal Québec, Canada;Department of Biology, University of Ottawa, Ontario, Canada;Sandia National Laboratories, Albuquerque, New Mexico;Department of Mathematics and Statistics, University of Ottawa, Ontario, Canada
Venue:
ISBRA'11 Proceedings of the 7th international conference on Bioinformatics research and applications
Year:
2011

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Abstract

A Maximum Agreement SubTree (MAST) is a largest subtree common to a set of trees and serves as a summary of common substructure in the trees. A single MAST can be misleading, however, since there can be an exponential number of MASTs, and two MASTs for the same tree set do not even necessarily share any leaves. In this paper we introduce the notion of the Kernel Agreement SubTree (KAST), which is the summary of the common substructure in all MASTs, and show that it can be calculated in polynomial time (for trees with bounded degree). Suppose the input trees represent competing hypotheses for a particular phylogeny. We show the utility of the KAST as a method to discern the common structure of confidence, and as a measure of how confident we are in a given tree set.