A Hungarian Algorithm for Error-Correcting Graph Matching
Abstract: Bipartite graph matching algorithms become more and more popular to solve error-correcting graph matching problems and to approximate the graph edit distance of two graphs. However, the memory requirements and execution times of this method are respectively proportional to \((n+m)^2\) and \((n+m)^3\) where n and m are the order of the graphs. Subsequent developments reduced these complexities. However, these improvements are valid only under some constraints on the parameters of the graph edit distance. We propose in this paper a new formulation of the bipartite graph matching algorithm designed to solve efficiently the associated graph edit distance problem. The resulting algorithm requires \(\mathcal {O}(nm)\) memory space and \(\mathcal {O}(\min (n,m)^2\max (n,m))\) execution times.
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