A Local Branching Heuristic for the Graph Edit Distance Problem.

In graph matching, Graph Edit Distance (GED) is a well-known distance measure for graphs and it is a NP-Hard minimization problem. Many heuristics are defined in the literature to give approximated solutions in a reasonable time. Some other work have used mathematical programming tools to come up with Mixed Integer Linear Program (MILP) models. In this work, a heuristic from Operational Research domain, is proposed and adapted to handle GED problem. It is called Local Branching and operates over a MILP model, where it defines neighborhoods in the solution space by adding the local branching constraint. A black-box MILP solver is then used to intensify the search in a neighborhood. This makes the solution search very fast, and allow exploring different sub-regions. Also, it includes a diversification mechanism to escape local solutions and in this work this mechanism is modified and improved. Finally, it is evaluated against other heuristics in order to show its efficiency and precision.