Fast Computation of the Tree Edit Distance between Unordered Trees Using IP Solvers
We propose a new method for computing the tree edit distance between two unordered trees by problem encoding. Our method transforms an instance of the computation into an instance of some IP problems and solves it by an efficient IP solver. The tree edit distance is defined as the minimum cost of a sequence of edit operations (either substitution, deletion, or insertion) to transform a tree into another one. Although its time complexity is NP-hard, some encoding techniques have been proposed for computational efficiency. An example is an encoding method using the clique problem. As a new encoding method, we propose to use IP solvers and provide new IP formulations representing the problem of finding the minimum cost mapping between two unordered trees, where the minimum cost exactly coincides with the tree edit distance. There are IP solvers other than that for the clique problem and our method can efficiently compute ariations of the tree edit distance by adding additional constraints. Our experimental results with Glycan datasets and the Web log datasets CSLOGS show that our method is much faster than an existing method if input trees have a large degree. We also show that two variations of the tree edit distance could be computed efficiently by IP solvers.
Keywordstree edit distance unordered tree IP formulation
Unable to display preview. Download preview PDF.
- 4.Bixby, R.E., Fenelon, M., Gu, Z., Rothberg, E., Wunderling, R.: Mixed integer programming: a progress report. In: The Sharpest Cut: The Impact of Manfred Padberg and His Work. MPS-SIAM Series on Optimization, vol. 4, pp. 309–326 (2004)Google Scholar
- 5.Daiji, F., Takeyuki, T., Atushiro, T., Etsuji, T., Tatsuya, A.: A clique-based method for the edit distance between unordered trees and its application to analysis of glycan structures. BMC Bioinformatics 12 (2011)Google Scholar
- 6.Griva, I., Nash, S.G., Sofer, A.: Linear and Nonlinear Optimization, 2nd edn. Society for Industrial Mathematics (2008)Google Scholar
- 9.IBM: IBM ILOG CPLEX Optimizer (2010), http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/
- 13.Kuboyama, T.: Matching and learning in trees. Ph.D Thesis (The University of Tokyo) (2007)Google Scholar
- 14.Mori, T., Tamura, T., Fukagawa, D., Takasu, A., Tomita, E., Akutsu, T.: An improved clique-based method for computing edit distance between rooted unordered trees. SIG-BIO 2011(3), 1–6 (2011)Google Scholar
- 17.Valiente, G.: An efficient bottom-up distance between trees. In: Proceedings of the 8th International Symposium of String Processing and Information Retrieval, pp. 212–219. Press (2001)Google Scholar