Speeding Up Graph Edit Distance Computation through Fast Bipartite Matching

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.

[1]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[2]  H. Kuhn The Hungarian method for the assignment problem , 1955 .

[3]  King-Sun Fu,et al.  A distance measure between attributed relational graphs for pattern recognition , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  Antonio Robles-Kelly,et al.  Graph edit distance from spectral seriation , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Wan-Jui Lee,et al.  A Labelled Graph Based Multiple Classifier System , 2009, MCS.

[6]  Romain Raveaux,et al.  A graph matching method and a graph matching distance based on subgraph assignments , 2010, Pattern Recognit. Lett..

[7]  Mauro Dell'Amico,et al.  8. Quadratic Assignment Problems: Algorithms , 2009 .

[8]  Francisco Escolano,et al.  Graph-Based Representations in Pattern Recognition, 6th IAPR-TC-15 International Workshop, GbRPR 2007, Alicante, Spain, June 11-13, 2007, Proceedings , 2007, GbRPR.

[9]  J. Munkres ALGORITHMS FOR THE ASSIGNMENT AND TRANSIORTATION tROBLEMS* , 1957 .

[10]  G. Dantzig On the Shortest Route Through a Network , 1960 .

[11]  Celso C. Ribeiro,et al.  A Randomized Heuristic for Scene Recognition by Graph Matching , 2004, WEA.

[12]  Horst Bunke,et al.  Inexact graph matching for structural pattern recognition , 1983, Pattern Recognit. Lett..

[13]  Christine Solnon,et al.  Reactive Tabu Search for Measuring Graph Similarity , 2005, GbRPR.

[14]  Horst Bunke,et al.  Graph Edit Distance with Node Splitting and Merging, and Its Application to Diatom Idenfication , 2003, GbRPR.

[15]  Edwin R. Hancock,et al.  Spectral embedding of graphs , 2003, Pattern Recognit..

[16]  Klaus Jansen,et al.  Experimental and Efficient Algorithms , 2003, Lecture Notes in Computer Science.

[17]  Mario Vento,et al.  Thirty Years Of Graph Matching In Pattern Recognition , 2004, Int. J. Pattern Recognit. Artif. Intell..

[18]  William J. Christmas,et al.  Structural Matching in Computer Vision Using Probabilistic Relaxation , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Ah Chung Tsoi,et al.  The Graph Neural Network Model , 2009, IEEE Transactions on Neural Networks.

[20]  Richard C. Wilson,et al.  Levenshtein distance for graph spectral features , 2004, ICPR 2004.

[21]  Mauro Dell'Amico,et al.  Assignment Problems , 1998, IFIP Congress: Fundamentals - Foundations of Computer Science.

[22]  Kaspar Riesen,et al.  Graph Classification and Clustering Based on Vector Space Embedding , 2010, Series in Machine Perception and Artificial Intelligence.

[23]  A. Volgenant,et al.  A shortest augmenting path algorithm for dense and sparse linear assignment problems , 1987, Computing.

[24]  Edwin R. Hancock,et al.  Inexact graph matching using genetic search , 1997, Pattern Recognit..

[25]  Alfred O. Hero,et al.  A binary linear programming formulation of the graph edit distance , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[26]  Kaspar Riesen,et al.  Approximate graph edit distance computation by means of bipartite graph matching , 2009, Image Vis. Comput..