Dynamic Graph Algorithms with Applications
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Exact ILP solutions for phylogenetic minimum flip problems
Proceedings of the First ACM International Conference on Bioinformatics and Computational Biology
Constructing the R* consensus tree of two trees in subcubic time
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Comparing and aggregating partially resolved trees
Theoretical Computer Science
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The inference of consensus from a set of evolutionary trees is a fundamental problem in a number of fields such as biology and historical linguistics, and many models for inferring this consensus have been proposed. In this paper we present a model for deriving what we call a local consensus tree T from a set of trees ${\cal T}$. The model we propose presumes a function f, called a total local consensus function, which determines for every triple A of species, the form that the local consensus tree should take on A. We show that all local consensus trees, when they exist, can be constructed in polynomial time and that many fundamental problems can be solved in linear time. We also consider partial local consensus functions and study optimization problems under this model. We present linear time algorithms for several variations. Finally we point out that the local consensus approach ties together many previous approaches to constructing consensus trees.