Graph Clustering Via QUBO and Digital Annealing

Abstract: This article empirically examines the computational cost of solving a known hard problem, graph clustering, using novel purpose-built computer hardware. We express the graph clustering problem as an intra-cluster distance or dissimilarity minimization problem. We formulate our poblem as a quadratic unconstrained binary optimization problem and employ a novel computer architecture to obtain a numerical solution. Our starting point is a clustering formulation from the literature. This formulation is then converted to a quadratic unconstrained binary optimization formulation. Finally, we use a novel purpose-built computer architecture to obtain numerical solutions. For benchmarking purposes, we also compare computational performances to those obtained using a commercial solver, Gurobi, running on conventional hardware. Our initial results indicate the purpose-built hardware provides equivalent solutions to the commercial solver, but in a very small fraction of the time required.