 
Summary: MAXIMUM AGREEMENT SUBTREE IN A SET OF
EVOLUTIONARY TREES Metrics and Efficient Algorithms \Lambda
Amihood Amir y Dmitry Keselman z
Georgia Tech Georgia Tech
and and
BarIlan University Simons Technologies
Abstract
The maximum agreement subtree approach is one method of reconciling different evolutionary trees
for the same set of species. An agreement subtree enables choosing a subset of the species for whom the
restricted subtree is equivalent (under a suitable definition) in all given evolutionary trees.
Recently, dynamic programming ideas were used to provide polynomial time algorithms for finding
a maximum homeomorphic agreement subtree of two trees. Generalizing these methods to sets of more
than two trees yields algorithms that are exponential in the number of trees. Unfortunately, it turns out
that in reality one is usually presented with more than two trees, sometimes as many as thousands of
trees.
In this paper we prove that the maximum homeomorphic agreement subtree problem is NPcomplete
for three trees with unbounded degrees. We then show an approximation algorithm of time O(kn 5 ) for
choosing the species that are not in a maximum agreement subtree of a set of k trees. Our approximation
is guaranteed to provide a set that is no more than 4 times the optimum solution.
While the set of evolutionary trees may be large in practice, the trees usually have very small degrees,
