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A Linear Programming Approach for the Weighted Graph Matching Problem
May 1993 (vol. 15 no. 5)
pp. 522-525

A linear programming (LP) approach is proposed for the weighted graph matching problem. A linear program is obtained by formulating the graph matching problem in L/sub 1/ norm and then transforming the resulting quadratic optimization problem to a linear one. The linear program is solved using a simplex-based algorithm. Then, approximate 0-1 integer solutions are obtained by applying the Hungarian method on the real solutions of the linear program. The complexity of the proposed algorithm is polynomial time, and it is O(n/sup 6/L) for matching graphs of size n. The developed algorithm is compared to two other algorithms. One is based on an eigendecomposition approach and the other on a symmetric polynomial transform. Experimental results showed that the LP approach is superior in matching graphs than both other methods.

[1] W. H. Tsai, and K. S. Fu, "Error-correcting isomorphisms of attributed relation graphs for pattern recognition,"IEEE Trans. Syst. Man Cybern., vol. SMC-9, pp. 757-768, Dec. 1979.
[2] L. Kitchen, "Relaxation applied to matching quantitative relational structures,"IEEE Trans. Syst. Man Cybern., vol. SMC-10, pp. 96-101, Feb. 1980.
[3] S. Umeyama, "An eigendecomposition approach to weighted graph matching problems,"IEEE Trans. Patt. Anal. Machine Intell., vol. 10, no. 5, pp. 695-703, Sept. 1988.
[4] M. R. Garey and D. S. Johnson,Computers and Intractability: A Guide to Theory of NP-Completeness. San Francisco, CA: Freeman, 1979.
[5] M. You and A. K. C. Wang, "An algorithm for graph optimal isomorphism," inProc. ICPR, 1984, pp. 316-319.
[6] L. Kitchen and A. Rosenfeld, "Discrete relaxation for matching relational structures,"IEEE Trans. Syst. Man Cybern., vol. SMC-9, pp. 869-864, Dec. 1979.
[7] H. A. Almohamad, "A polynomial transform for matching pairs of weighted graphs,"J. Applied Math. Modeling, vol. 15, no. 4, Apr. 1991.
[8] M. Bazaraa, J. Jarvis, and H. Sherali,Linear Programming and Network Flows. New York: Wiley, 1990.
[9] A. Charnes and W. W. Cooper,Management models and industrial applications of linear programming, Vol. 1. New York: Wiley, 1963.
[10] C. C. Gonzaga, "An algorithm for solving linear programming programs inO(n3L) operation," inProgress in Mathematical Programming, Interior Point and Related Methods(N. Megiddo, Ed.). New York: Springer-Verlag, 1988.
[11] C. H. Papadimitriou and K. Steiglitz,Combinatorial Optimization: Algorithms and Complexity. Englewood Cliffs, NJ: Prentice-Hall, 1982.
[12] D. Dubois and H. Prade,Fuzzy Sets and Systems: Theory and Applications. New York: Academic, 1980.

Index Terms:
computational complexity; linear programming; weighted graph matching; quadratic optimization; simplex-based algorithm; Hungarian method; polynomial time; eigendecomposition; symmetric polynomial transform; computational complexity; linear programming; pattern recognition
Citation:
H.A. Almohamad, S.O. Duffuaa, "A Linear Programming Approach for the Weighted Graph Matching Problem," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 5, pp. 522-525, May 1993, doi:10.1109/34.211474
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