Determining the Hausdorff Distance Between Trees in Polynomial Time

TL;DR

This paper introduces a polynomial-time recursive algorithm for computing the Hausdorff distance between trees, leveraging divide and conquer and maximum bipartite matching techniques.

Contribution

It provides the first known efficient algorithm for calculating the Hausdorff distance between trees, a previously unresolved problem.

Findings

Polynomial-time algorithm for Hausdorff distance between trees

Uses divide and conquer and bipartite matching techniques

Algorithm complexity is polynomial

Abstract

The Hausdorff distance is a relatively new measure of similarity of graphs. The notion of the Hausdorff distance considers a special kind of a common subgraph of the compared graphs and depends on the structural properties outside of the common subgraph. There was no known efficient algorithm for the problem of determining the Hausdorff distance between two trees, and in this paper we present a polynomial-time algorithm for it. The algorithm is recursive and it utilizes the divide and conquer technique. As a subtask it also uses the procedure that is based on the well known graph algorithm of finding the maximum bipartite matching.