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<p><b>Abstract</b>—A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated nonconvexity, two-way (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational complexity [<it>O</it>(<it>lm</it>), where <it>l</it> and <it>m</it> are the number of links in the two graphs] and robustness in the presence of noise offer advantages over traditional combinatorial approaches. The algorithm, not restricted to any special class of graph, is applied to subgraph isomorphism, weighted graph matching, and attributed relational graph matching. To illustrate the performance of the algorithm, attributed relational graphs derived from objects are matched. Then, results from twenty-five thousand experiments conducted on 100 node random graphs of varying types (graphs with only zero-one links, weighted graphs, and graphs with node attributes and multiple link types) are reported. No comparable results have been reported by any other graph matching algorithm before in the research literature. Twenty-five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated.</p>
Graduated assignment, continuation method, graph matching, weighted graphs, attributed relational graphs, softassign, model matching, relaxation labeling.

A. Rangarajan and S. Gold, "A Graduated Assignment Algorithm for Graph Matching," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 18, no. , pp. 377-388, 1996.
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