Abstract
The problem of graph matching is usually approached via explicit search in state-space or via energy minimization. In this paper we deal with a class of heuristics coming from a combination of both approaches. Combinatorially, the basic heuristic of the class can be interpreted as a greedy algorithm to form maximal cliques in an association graph. To avoid one of the main drawbacks of greedy strategies, i.e. that they are easily fooled by poor local optima, we propose a modification which allows for vertex swaps during the formation of a clique. Experiments on random graphs show the effectiveness of the proposed heuristics both in terms of quality of solutions and speed.
This work is supported by the Austrian Science Foundation (FWF) under grant P14445-MAT and by MURST under grant MM09308497.
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References
A. P. Ambler et al. A versatile computer-controlled assembly system. In Proc. of 3rd Int. J. Conf. Art. Intell., pages 298–307, 1973.
H. G. Barrow and R. M. Burstall. Subgraph isomorphism, matching relational structures and maximal cliques. Inform. Process. Lett., 4(4):83–84, 1976.
R. Battiti and M. Protasi. Reactive local search for the maximum clique problem. Algorithmica, 29:610–637, 2001.
I. M. Bomze, M. Budinich, M. P. Pardalos, and M. Pelillo. The maximum clique problem. In D.-Z. Du and P. M. Pardalos, editors, Handbook of Combinatorial Optimization (Suppl. Vol. A), pages 1–74. Kluwer, Boston, MA, 1999.
M. Brockington and J. C. Culberson. Camouflaging independent sets in quasi-random graphs. In D. Johnson and M. A. Trick, editors, Cliques, Coloring and Satisfiability, volume 26 of DIMACS series in Discrete Mathematics and Theoretical Computer Science, pages 75–88. Americ. Math. Soc., 1996.
C. Bron and J. Kerbosch. Algorithm457: Finding all cliques of an undirected graph. Comm. ACM, 16:575–577, 1973.
H. Bunke. Recent developments in graph matching. In A. Sanfeliu, J. Villanueva, M. Vanrell, R. Alquezar, A. Jain, and J. Kittler, editors, Proc. 15th Int. Conf. Pattern Recognition, volume 2, pages pp. 117–124. IEEE Computer Society, 2000.
R. W. Cottle, J.-S. Pang, and R. E. Stone. The Linear Complementarity Problem. Accademic Press, Boston, MA, 1992.
S. Gold and A. Rangarajan. A Graduated Assignment Algorithm for Graph Matching. IEEE Trans. Pattern Anal. and Machine Intell., 18(4):377–388, 1996.
S. Z. Li. Matching: invariant to translations, rotations and scale changes. Pattern Recogognition, 25(6):583–594, 1992.
M. Locatelli, I. M. Bomze, and M. Pelillo. Swaps, diversification, and the combinatorics of pivoting for the maximum weight clique. Technical Report CS-2002-12, Dipartimento di Informatica, Università Ca’ Foscari di Venezia, 30172 Venezia Mestre, Italy, 2002.
A. Massaro and M. Pelillo. Matching graphs by pivoting. Pattern Recognition Letters, 24:1099–1106, 2003.
A. Massaro, M. Pelillo, and I. M. Bomze. A complementary pivoting approach to the maximum weight clique problem. SIAM Journal on Optimization, 12(4):928–948, 2002.
B. Messmer and H. Bunke. A New Algorithm for Error-Tolerant Subgraph Isomorphism Detection. IEEE Trans. on Pattern Analysis and Machine Intelligence, 20(7):493–504, 1998.
T. S. Motzkin and E. G. Straus. Maxima for graphs and a new proof of a theorem of Turán. Cand. J. Math., 17:533–540, 1965.
M. Pelillo. A unifying framework for relational structure matching. In A. K. Jain, S. Venkatesh, and B. C. Lovell, editors, Proc. 14th Int. Conf. Pattern Recognition, pages 1316–1319. IEEE-Computer Society Press, 1998.
M. Pelillo. Replicator equations, maximal cliques, and graph isomorphism. Neural Computation, 11:1933–1955, 1999.
M. Pelillo. Matching free trees, maximal cliques, and monotone game dynamics. IEEE Trans. Pattern Anal. and Machine Intell., 24(11):1535–1541, 2002.
M. Pelillo, K. Siddiqi, and S. W. Zucker. Matching Hierarchical Structures Using Association Graphs. IEEE Trans. Pattern Anal. and Machine Intell., 21(11):1105–1120, 1999.
L. G. Shapiro and R. M. Haralick. Structural descriptions and inexact matching. IEEE Trans. Pattern Anal. and Machine Intell., 3:504–519, 1981.
W. H. Tsai and K. S. Fu. Subgraph error-correcting isomorphisms for syntactic pattern recognition. IEEE Trans. Syst. Man Cybern., 13:48–62, 1983.
R. C. Wilson and E. R. Hancock. Structural Matching by Discrete Relaxation. Trans. Pattern Anal. Machince Intell., 19(6):634–648, 1997.
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Fosser, P., Glantz, R., Locatelli, M., Pelillo, M. (2003). Swap Strategies for Graph Matching. In: Hancock, E., Vento, M. (eds) Graph Based Representations in Pattern Recognition. GbRPR 2003. Lecture Notes in Computer Science, vol 2726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45028-9_13
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DOI: https://doi.org/10.1007/3-540-45028-9_13
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