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Kaikoura Tree Theorems: Computing The Maximum Agreement Subtree

Summary: Kaikoura Tree Theorems: Computing The
Maximum Agreement Subtree
Mike Steel  Tandy Warnow y
February 11, 2003
The Maximum Agreement Subtree Problem was posed by Finden and
Gordon in 1985 [2], and is as follows: given a set S = fs1 ; s2 ; : : : ; sng and
two trees P and Q leaf-labelled by the elements of S, nd a maximum
cardinality subset S0 of S such that P jS0 = QjS0 . This problem arises
in evolutionary tree construction, where di erent methods or data yield
(possibly) di erent trees for the same species set, and the problem is to de-
termine the largest set of species on which the trees agree. An exponential
time algorithm for nding the maximum agreement subtree of two binary
trees was found by Kubicka et. al. [4]. In this paper, we will present
an O(n 4:5 (n 2 )) algorithm to determine the largest agreement subtree of
two trees. For the case of trees of maximum degree k, the algorithm has
running time O(n 2 (n 2 )).
1 Preliminary De nitions
We begin with some de nitions. A tree T is a connected acyclic graph. Given a
nite set S = fs 1 ; s 2 ; : : : ; s n g, we say that a tree T is leaf-labelled by S if there is


Source: Amir, Amihood - Computer Science Department, Bar Ilan University


Collections: Mathematics