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<p>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.</p>
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
S.O. Duffuaa, H.A. Almohamad, "A Linear Programming Approach for the Weighted Graph Matching Problem", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 15, no. , pp. 522-525, May 1993, doi:10.1109/34.211474
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