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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.

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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
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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