Solving the Graph Edit Distance Problem with Variable Partitioning Local Search

Abstract

In the world of graph matching, the Graph Edit Distance (GED) problem is a well-known distance measure between graphs. It has been proven to be a $$\mathcal {NP}$$ -hard minimization problem. This paper presents an adapted version of Variable Partitioning Local Search (VPLS) matheuristic for solving the GED problem. The main idea in VPLS is to perform local searches in the solution space of a Mixed Integer Linear Program (MILP). A local search is done in a small neighborhood defined based on a set of special variables. Those special variables are selected based on a procedure that extracts useful characteristics from the instance at hand. This actually ensures that the neighborhood contains high quality solutions. Finally, the experimentation results have shown that VPLS has outperformed existing heuristics in terms of solution quality on CMU-HOUSE database.