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International Journal of Combinatorics
Volume 2012 (2012), Article ID 908356, 18 pages
A Convex Relaxation Bound for Subgraph Isomorphism
Independent Research, 7052 Trondheim, Tyholtveien 68, Norway
Received 31 August 2011; Accepted 27 December 2011
Academic Editor: Liying Kang
Copyright © 2012 Christian Schellewald. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. R. Ullmann, “An algorithm for subgraph isomorphism,” Journal of the Association for Computing Machinery, vol. 23, no. 1, pp. 31–42, 1976.
- H. G. Barrow and R. M. Burstall, “Subgraph isomorphism, matching relational structures and maximal cliques,” Information Processing Letters, vol. 4, no. 4, pp. 83–84, 1976.
- B. T. Messmer and H. Bunke, “A new algorithm for error-tolerant subgraph isomorphism detection,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 5, pp. 493–504, 1998.
- D. Eppstein, “Subgraph isomorphism in planar graphs and related problems,” Journal of Graph Algorithms and Applications, vol. 3, no. 3, pp. 1–27, 1999.
- H. Bunke, “Error correcting graph matching: on the influence of the underlying cost function,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 9, pp. 917–922, 1999.
- A. Sanfeliu and K. S. Fu, “A distance measure between attributed relational graphs for pattern recognition,” IEEE Transactions on Systems, Man and Cybernetics, vol. 13, no. 3, pp. 353–362, 1983.
- Y.-K. Wang, K.-C. Fan, and J.-T. Horng, “Genetic-based search for error-correcting graph isomorphism,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 27, no. 4, pp. 588–597, 1997.
- H. Wolkowicz, R. Saigal, and L. Vandenberghe, Eds., Handbook of Semidefinite Programming, Kluwer Academic Publishers, Boston, Mass, USA, 2000.
- M. X. Goemans and D. P. Williamson, “Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming,” Journal of the Association for Computing Machinery, vol. 42, no. 6, pp. 1115–1145, 1995.
- J. Keuchel, C. Schnörr, C. Schellewald, and D. Cremers, “Binary partitioning, perceptual grouping, and restoration with semidefinite programming,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 11, pp. 1364–1379, 2003.
- C. Schellewald and C. Schnörr, “Probabilistic subgraph matching based on convex relaxation,” in Proceedings of the 5th International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR '05), vol. 3757 of Lecture Notes in Computer Science, pp. 171–186, 2005.
- H. Yu and E. R. Hancock, “Graph seriation using semi-definite programming,” in Proceedings of the 5th IAPR International Workshop on Graph-Based Representations in Pattern Recognition (GbRPR '05), vol. 3434 of Lecture Notes in Computer Science, pp. 63–71, 2005.
- M. Agrawal and L. S. Davis, “Camera calibration using spheres: a semi-definite programming approach,” in Proceedings of the 9th IEEE International Conference on Computer Vision (ICCV '03), vol. 2, pp. 782–789, 2003.
- I. M. Bomze, M. Budinich, P. M. Pardalos, and M. Pelillo, “The maximum clique problem,” in Handbook of Combinatorial Optimization, D.-Z. Du and P. M. Pardalos, Eds., pp. 1–74, Kluwer Academic, Boston, Mass, USA, 1999.
- M. Pelillo, “Replicator equations, maximal cliques, and graph isomorphism,” Neural Computation, vol. 11, no. 8, pp. 1933–1955, 1999.
- M. R. Garey and D. S. Johnson, Computers and Intractability, A Guide to the Theory of NP-Completeness, W. H. Freeman and Company, San Francisco, Calif, USA, 1991.
- P. M. Pardalos and S. A. Vavasis, “Quadratic programming with one negative eigenvalue is NP-hard,” Journal of Global Optimization, vol. 1, no. 1, pp. 15–22, 1991.
- B. Borchers, “CSDP, a C library for semidefinite programming,” Optimization Methods and Software, vol. 11, no. 1, pp. 613–623, 1999.
- S. J. Benson and Y. Ye, “DSDP3: dual scaling algorithm for general positive semidefinite programming,” Tech. Rep. ANL/MCS-P851-1000, Argonne National Labs, 2001.
- M. Kočvara and M. Stingl, “Pennon: a code for convex nonlinear and semidefinite programming,” Optimization Methods & Software, vol. 18, no. 3, pp. 317–333, 2003.
- A. Graham, Kronecker Products and Matrix Calculus with Applications, Ellis Horwood and John Wiley & Sons, 1981.
- Y. Ye, Interior Point Algorithms: Theory and Analysis, John Wiley & Sons Inc., New York, NY, USA, 1997.
- H. D. Mittelmann, “An independent benchmarking of SDP and SOCP solvers,” Mathematical Programming Series B, vol. 95, no. 2, pp. 407–430, 2003.
- C. Helmberg, F. Rendl, R. J. Vanderbei, and H. Wolkowicz, “An interior-point method for semidefinite programming,” SIAM Journal on Optimization, vol. 6, no. 2, pp. 342–361, 1996.
- Brian Borchers. CSDP 4.8 User’s Guide, 2004.
- M. Budinich, “Exact bounds on the order of the maximum clique of a graph,” Discrete Applied Mathematic, vol. 127, no. 3, pp. 535–543, 2003.
- T. S. Motzkin and E. G. Straus, “Maxima for graphs and a new proof of a theorem of Turán,” Canadian Journal of Mathematics. Journal Canadien de Mathématiques, vol. 17, pp. 533–540, 1965.
- L. P. Cordella, P. Foggia, C. Sansone, and M. Vento, “Performance evaluation of the vf graph matching algorithm,” in Proceedings of the 10th International Conference on Image Analysis and Processing (ICIAP ’99), p. 1172, IEEE Computer Society, Washington, DC, USA, 1999.