Graph Partitioning with Fujitsu Digital Annealer

Abstract

Graph partitioning, or community detection, is the cornerstone of many fields, such as logistics, transportation and smart power grids. Efficient computation and efficacious evaluation of communities are both essential, especially in commercial and industrial settings. However, the solution space of graph partitioning increases drastically with the number of vertices and subgroups. With an eye to solving large scale graph partitioning and other optimization problems within a short period of time, the Digital Annealer (DA), a specialized CMOS hardware also featuring improved algorithms, has been devised by Fujitsu Ltd. This study gauges Fujitsu DA's performance and running times. The modularity was implemented as both the objective function and metric for the solutions. The graph partitioning problems were formatted into Quadratic Unconstrained Binary Optimization (QUBO) structures so that they could be adequately imported into the DA. The DA yielded the highest modularity among other studies when partitioning Karate Club, Les Miserables, American Football, and Dolphin. Moreover, the DA was able to partition the Case 1354pegase power grid network into 45 subgroups, calling for 60,930 binary variables, whilst delivering optimal modularity results within a solving time of roughly 80 seconds. Our results suggest that the Fujitsu DA can be applied for rapid and efficient optimization for graph partitioning