Skip to main content

Swap Strategies for Graph Matching

  • Conference paper
  • First Online:
Graph Based Representations in Pattern Recognition (GbRPR 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2726))

  • 569 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. P. Ambler et al. A versatile computer-controlled assembly system. In Proc. of 3rd Int. J. Conf. Art. Intell., pages 298–307, 1973.

    Google Scholar 

  2. H. G. Barrow and R. M. Burstall. Subgraph isomorphism, matching relational structures and maximal cliques. Inform. Process. Lett., 4(4):83–84, 1976.

    Article  MATH  Google Scholar 

  3. R. Battiti and M. Protasi. Reactive local search for the maximum clique problem. Algorithmica, 29:610–637, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  4. 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.

    Google Scholar 

  5. 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.

    Google Scholar 

  6. C. Bron and J. Kerbosch. Algorithm457: Finding all cliques of an undirected graph. Comm. ACM, 16:575–577, 1973.

    Article  MATH  Google Scholar 

  7. 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.

    Google Scholar 

  8. R. W. Cottle, J.-S. Pang, and R. E. Stone. The Linear Complementarity Problem. Accademic Press, Boston, MA, 1992.

    MATH  Google Scholar 

  9. S. Gold and A. Rangarajan. A Graduated Assignment Algorithm for Graph Matching. IEEE Trans. Pattern Anal. and Machine Intell., 18(4):377–388, 1996.

    Article  Google Scholar 

  10. S. Z. Li. Matching: invariant to translations, rotations and scale changes. Pattern Recogognition, 25(6):583–594, 1992.

    Article  Google Scholar 

  11. 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.

    Google Scholar 

  12. A. Massaro and M. Pelillo. Matching graphs by pivoting. Pattern Recognition Letters, 24:1099–1106, 2003.

    Article  MATH  Google Scholar 

  13. 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.

    Article  MATH  MathSciNet  Google Scholar 

  14. 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.

    Article  Google Scholar 

  15. 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.

    MATH  MathSciNet  Google Scholar 

  16. 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.

    Google Scholar 

  17. M. Pelillo. Replicator equations, maximal cliques, and graph isomorphism. Neural Computation, 11:1933–1955, 1999.

    Article  Google Scholar 

  18. M. Pelillo. Matching free trees, maximal cliques, and monotone game dynamics. IEEE Trans. Pattern Anal. and Machine Intell., 24(11):1535–1541, 2002.

    Article  Google Scholar 

  19. 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.

    Article  Google Scholar 

  20. L. G. Shapiro and R. M. Haralick. Structural descriptions and inexact matching. IEEE Trans. Pattern Anal. and Machine Intell., 3:504–519, 1981.

    Article  Google Scholar 

  21. W. H. Tsai and K. S. Fu. Subgraph error-correcting isomorphisms for syntactic pattern recognition. IEEE Trans. Syst. Man Cybern., 13:48–62, 1983.

    MATH  MathSciNet  Google Scholar 

  22. R. C. Wilson and E. R. Hancock. Structural Matching by Discrete Relaxation. Trans. Pattern Anal. Machince Intell., 19(6):634–648, 1997.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/3-540-45028-9_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40452-1

  • Online ISBN: 978-3-540-45028-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics