COMPUTING THE LOCAL CONSENSUS OF TREES

The inference of consensus from a set of evolutionary trees is a funda mental problem in a number of fields such as biology and historical li nguistics, and many models for inferring this consensus have been prop osed. In this paper we present a model for deriving what we call a loc al consensus tree T from a set of trees T. The model we propose presum es a function f, called a total local consensus function, which determ ines 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 th ey exist, can be constructed in polynomial time and that many fundamen tal problems can be solved in linear time. We also consider partial lo cal consensus functions and study optimization problems under this mod el. We present linear time algorithms for several variations. Finally we point out that the local consensus approach ties together many prev ious approaches to constructing consensus trees.