An Even Faster and More Unifying Algorithm for Comparing Trees via Unbalanced Bipartite Matchings

TL;DR

This paper introduces a faster, more general algorithm for comparing labeled trees using unbalanced bipartite matchings, improving efficiency over previous methods and extending applicability to arbitrarily labeled trees.

Contribution

It presents a novel, faster algorithm for maximum agreement subtree comparison that handles arbitrarily labeled trees and improves bipartite matching for unbalanced graphs.

Findings

Algorithm is faster than previous methods for tree comparison.

New matching algorithm handles unbalanced graphs efficiently.

Applicable to arbitrary labeled trees, broadening scope of comparison.

Abstract

A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees. Previous work on this similarity measure is only concerned with the comparison of labeled trees of two special kinds, namely, uniformly labeled trees (i.e., trees with all their nodes labeled by the same symbol) and evolutionary trees (i.e., leaf-labeled trees with distinct symbols for distinct leaves). This paper presents an algorithm for comparing trees that are labeled in an arbitrary manner. In addition to this generality, this algorithm is faster than the previous algorithms. Another contribution of this paper is on maximum weight bipartite matchings. We show how to speed up the best known matching algorithms when the input graphs are node-unbalanced or weight-unbalanced. Based on these enhancements, we obtain an efficient algorithm for a new matching problem called the hierarchical bipartite matching problem, which is at the core of our maximum agreement subtree algorithm.