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.
Funding by the German Research Foundation (DFG) under grant number PA 3460/2-1 is gratefully acknowledged.
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Notes
- 1.
Note that we use ‘node’ and ‘label’ interchangeably in this paper. To disambiguate between two nodes with the same label, we use the index.
- 2.
Strictly speaking, this is only valid if the lower bound f is exact for insertions. This is the case for all heuristics considered in this paper.
- 3.
We also tested lower K, which achieved worse results for all methods.
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Paaßen, B. (2021). An A*-algorithm for the Unordered Tree Edit Distance with Custom Costs. In: Reyes, N., et al. Similarity Search and Applications. SISAP 2021. Lecture Notes in Computer Science(), vol 13058. Springer, Cham. https://doi.org/10.1007/978-3-030-89657-7_27
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DOI: https://doi.org/10.1007/978-3-030-89657-7_27
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