Chapter

Graph-Based Representations in Pattern Recognition

Volume 6658 of the series Lecture Notes in Computer Science pp 102-111

Speeding Up Graph Edit Distance Computation through Fast Bipartite Matching

  • Stefan FankhauserAffiliated withInstitute of Computer Science and Applied Mathematics, University of Bern
  • , Kaspar RiesenAffiliated withInstitute of Computer Science and Applied Mathematics, University of Bern
  • , Horst BunkeAffiliated withInstitute of Computer Science and Applied Mathematics, University of Bern

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Abstract

In the field of structural pattern recognition graphs constitute a very common and powerful way of representing objects. The main drawback of graph representations is that the computation of various graph similarity measures is exponential in the number of involved nodes. Hence, such computations are feasible for rather small graphs only. One of the most flexible graph similarity measures is graph edit distance. In this paper we propose a novel approach for the efficient computation of graph edit distance based on bipartite graph matching by means of the Volgenant-Jonker assignment algorithm. Our proposed algorithm provides only suboptimal edit distances, but runs in polynomial time. The reason for its sub-optimality is that edge information is taken into account only in a limited fashion during the process of finding the optimal node assignment between two graphs. In experiments on diverse graph representations we demonstrate a high speed up of our proposed method over a traditional algorithm for graph edit distance computation and over two other sub-optimal approaches that use the Hungarian and Munkres algorithm. Also, we show that classification accuracy remains nearly unaffected by the suboptimal nature of the algorithm.