Abstract
We present a neural network approach to solve exact and inexact graph isomorphism problems for weighted graphs. In contrast to other neural heuristics or related methods our approach is based on approximating the automorphism partition of a graph to reduce the search space followed by an energy-minimizing matching process. Experiments on random graphs with 100–5000 vertices are presented and discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Abdulrahim and M. Misra. A graph isomorphism algorithm for object recognition. Pattern Analysis and Application, 1(3):189–201, 1998.
A.P. Ambler, H.G. Barrow, C.M. Brown, R.M. Burstall, and R. J. Popplestone. A versatile computer-controlled assembly system. In International Joint Conference on Artificial Intelligence, pages 298–307. Stanford University, California, 1973.
L. Babai, P. Erdös, and S. Selkow. Random graph isomorphism. SIAM Journal on Computing, 9:628–635, 1980.
D.G. Corneil and D.G. Kirkpatrick. A theoretical analysis of various heuristics for the graph isomorphism problem. SIAM Journal of Computing, 9(2):281–297, 1980.
B.J. Jain and F. Wysotzki. Fast winner-takes-all networks for the maximum clique problem. In 25th German Conference on Artificial Intelligence, pages 163–173. Springer, 2002.
H.L. Morgan. The generation of a unique machine description for chemical structures. Journal of Chemical Documentation, 5:107–112, 1965.
M. Pelillo. Replicator equations, maximal cliques, and graph isomorphism. Neural Computation, 11(8):1933–1955, 1999.
M. Pelillo, K. Siddiqi, and S.W. Zucker. Matching hierarchical structures using association graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(11):1105–1120, 1999.
A. Rangarajan, S. Gold, and E. Mjolsness. A novel optimizing network architecture with applications. Neural Computation, 8(5):1041–1060, 1996.
A. Rangarajan and E. Mjolsness. A Lagrangian relaxation network for graph matching. IEEE Transactions on Neural Networks, 7(6):1365–1381, 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jain, B.J., Wysotzki, F. (2003). A Novel Neural Network Approach to Solve Exact and Inexact Graph Isomorphism Problems. In: Kaynak, O., Alpaydin, E., Oja, E., Xu, L. (eds) Artificial Neural Networks and Neural Information Processing — ICANN/ICONIP 2003. ICANN ICONIP 2003 2003. Lecture Notes in Computer Science, vol 2714. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44989-2_36
Download citation
DOI: https://doi.org/10.1007/3-540-44989-2_36
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40408-8
Online ISBN: 978-3-540-44989-8
eBook Packages: Springer Book Archive