Unbalanced and hierarchical bipartite matchings with applications to labeled tree comparison

Abstract

This paper is concerned with maximum weight matchings of bipartite graphs. We show how to speed up the existing matching algorithms when the input graphs are node unbalanced or weight unbalanced. Based on these improved matching algorithms, we can solve efficiently a new matching problem called the hierarchical bipartite matching problem, and thus obtain a simple and faster algoirthm for finding the maximum agreement subtree of two labeled trees. The significance of our subtree algorithm lies in the fact that it matches or outperforms all previously known subtree algorithms that were designed for two special cases of labeled trees, namely, uniformly labeled trees and evolutionary trees.