A parallel graph edit distance algorithm

Abstract

Graph edit distance (GED) has emerged as a powerful and flexible graph matching paradigm that can be used to address different tasks in pattern recognition, machine learning, and data mining. GED is an error-tolerant graph matching problem which consists in minimizing the cost of the sequence that transforms a graph into another by means of edit operations. Edit operations are deletion, insertion and substitution of vertices and edges. Each vertex/edge operation has its associated cost defined in the vertex/edge cost function. Unfortunately, Unfortunately, the GED problem is NP-hard. The question of elaborating fast and precise algorithms is of first interest. In this paper, a parallel algorithm for exact GED computation is proposed. Our proposal is based on a branch-and-bound algorithm coupled with a load balancing strategy. Parallel threads run a branch-and-bound algorithm to explore the solution space and to discard misleading partial solutions. In the mean time, the load balancing scheme ensures that no thread remains idle. Experiments on 4 publicly available datasets empirically demonstrated that under time constraints our proposal can drastically improve a sequential approach and a naive parallel approach. Our proposal was compared to 6 other methods and provided more precise solutions while requiring a low memory usage.