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Graph edit distance (GED) is a powerful and flexible graph matching paradigmthat can be used to address different tasks in structural pattern recognition,machine learning, and data mining. In this paper, some new binary linearprogramming formulations for computing the exact GED between two graphs areproposed. A major strength of the formulations lies in their genericity sincethe GED can be computed between directed or undirected fully attributed graphs(i.e. with attributes on both vertices and edges). Moreover, a relaxation ofthe domain constraints in the formulations provides efficient lower boundapproximations of the GED. A complete experimental study comparing the proposedformulations with 4 state-of-the-art algorithms for exact and approximate graphedit distances is provided. By considering both the quality of the proposedsolution and the efficiency of the algorithms as performance criteria, theresults show that none of the compared methods dominates the others in thePareto sense. As a consequence, faced to a given real-world problem, atrade-off between quality and efficiency has to be chosen w.r.t. theapplication constraints. In this context, this paper provides a guide that canbe used to choose the appropriate method.

Graph edit distance : a new binary linear programming formulation