An A*-algorithm for the Unordered Tree Edit Distance with Custom Costs

TL;DR

This paper introduces three new heuristics for the A* algorithm to compute unordered tree edit distances with custom costs, enhancing efficiency and accuracy in chemical data analysis.

Contribution

It presents novel heuristics for A* that accommodate custom cost functions, enabling better domain-specific distance computations.

Findings

Custom heuristics improve A* speed on chemical datasets.

Using custom costs enhances the accuracy of property prediction.

Polynomial edit distances perform comparably to unordered tree edit distances.

Abstract

The unordered tree edit distance is a natural metric to compute distances between trees without intrinsic child order, such as representations of chemical molecules. While the unordered tree edit distance is MAX SNP-hard in principle, it is feasible for small cases, e.g. via an A* algorithm. Unfortunately, current heuristics for the A* algorithm assume unit costs for deletions, insertions, and replacements, which limits our ability to inject domain knowledge. In this paper, we present three novel heuristics for the A* algorithm that work with custom cost functions. In experiments on two chemical data sets, we show that custom costs make the A* computation faster and improve the error of a 5-nearest neighbor regressor, predicting chemical properties. We also show that, on these data, polynomial edit distances can achieve similar results as the unordered tree edit distance.