Abstract
The RW algorithm has been proposed recently to solve the exact graph matching problem. This algorithm exploits Random Walk theory to compute a topological signature which can be used to match the nodes in two isomorphic graphs. However, the algorithm may suffer from the presence of colliding signatures in the same graph, which may prevent the procedure from finding the complete mapping between the matching nodes. In this paper we propose an improved version of the original algorithm, the RW2 algorithm, which progressively expands the node signatures by a recursive visit of the node descendants and ancestors to disambiguate the colliding signatures. The experimental results, performed on a benchmark dataset, show that the new algorithm attains a better matching rate with almost the same computational cost as the original one.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Conte, D., Foggia, P., Sansone, P., Vento, M.: Thirty years of graph matching in pattern recognition. International Journal of Pattern Recognition and Artificial Intelligence 18, 265–298 (2004)
Ullmann, J.: An algorithm for subgraph isomorphism. Journal of the Association for Computing Machinery 23, 31–42 (1976)
Schmidt, D., Druffel, L.: A fast backtracking algorithm to test directed graphs for isomorphism using distance matrices. Journal of the Association for Computing Machinery 23, 433–445 (1976)
Cordella, L., Foggia, P., Sansone, C., Vento, M.: Evaluation performance of the VF graph matching algorithm. In: Proceedings of the 10th International Conference on Image Analysis and Processing, pp. 1172–1177. IEEE Computer Society Press, Los Alamitos (1999)
McKay, B.D.: Practical graph isomorphism. Congressus Numerantium 30, 45–87 (1981)
Foggia, P., Sansone, C., Vento, M.: A database of graphs for isomorphism and sub–graph isomorphism benchmarking. In: Proceedings of the 3rd IAPR TC–15 International Workshop on Graph–based Representation (2001)
Gori, M., Maggini, M., Sarti, L.: Graph matching using random walks. In: Proceedings of the International Conference on Pattern Recongition, Cambridge, UK, vol. 3, pp. 394–397 (2004)
Umeyama, S.: An eigen–decomposition approach to weighted graph matching problem. IEEE Transactions on Pattern Analysis and Machine Intelligence 10–5, 695–703 (1988)
Robles-Kelly, A., Hancock, E.: String edit distance, random walks and graph matching. International Journal of Pattern Recognition and Artificial Intelligence 18, 315–327 (2004)
Robles-Kelly, A., Hancock, E.: Graph edit distance from spectral seriation. IEEE Transactions on Pattern Analysis and Machine Intelligence 27, 365–378 (2005)
Gori, M., Maggini, M., Sarti, M., L.: Exact and approximate graph matching using random walks. IEEE Transactions on Pattern Analysis and Machine Intelligence (2005) (To appear)
Seneta, E.: Non-negative matrices and Markov chains. Springer, Heidelberg (1981)
Bianchini, M., Gori, M., Scarselli, F.: Inside pagerank. ACM Transactions on Internet Technology 5 (2005)
Foggia, P., Sansone, C., Vento, M.: A performance comparison of five algorithms for graph isomorphism. In: Proceedings of the 3rd IAPR TC–15 International Workshop on Graph–based Representation. IEEE Computer Society Press, Los Alamitos (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gori, M., Maggini, M., Sarti, L. (2005). The RW2 Algorithm for Exact Graph Matching. In: Singh, S., Singh, M., Apte, C., Perner, P. (eds) Pattern Recognition and Data Mining. ICAPR 2005. Lecture Notes in Computer Science, vol 3686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11551188_9
Download citation
DOI: https://doi.org/10.1007/11551188_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28757-5
Online ISBN: 978-3-540-28758-2
eBook Packages: Computer ScienceComputer Science (R0)