# Improved Methods for Computing Distances between Unordered Trees Using Integer Programming

## TL;DR

This paper introduces improved integer programming formulations for computing distances between unordered trees, leveraging dynamic programming and bipartite matching, resulting in significantly enhanced computational performance.

## Contribution

The authors develop new integer programming models for tree distances that are more efficient, dividing problems into smaller subproblems and reducing constraints compared to prior methods.

## Key findings

- Significant performance improvements over previous methods
- Reduced number of subproblems and constraints
- Efficient polynomial-time solutions for certain distances

## Abstract

Kondo et al. (DS 2014) proposed methods for computing distances between unordered rooted trees by transforming an instance of the distance computing problem into an instance of the integer programming problem. They showed that the tree edit distance, segmental distance, and bottom-up segmental distance problem can be respectively transformed into an integer program which has $O(nm)$ variables and $O(n^2m^2)$ constraints, where $n$ and $m$ are the number of nodes of input trees. In this work, we propose new integer programming formulations for these three distances and the bottom-up distance by applying dynamic programming approach. We divide the tree edit distance problem into $O(nm)$ subproblems each of which has only $O(n + m)$ constraints. For the other three distances, each subproblem can be reduced to a maximum weighted matching problem in a bipartite graph which can be solved in polynomial time. In order to evaluate our methods, we compare our method to the previous one due to Kondo et al. The experimental results show that the performance of our methods have been improved remarkably compared to that of the previous method.