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.

Benchmarking Quantum(-inspired) Annealing Hardware on Practical Use Cases

“…The Fujitsu Digital Annealer (DA) has also been applied to a purely scientific problem, e.g. maximum clique problem Naghsh et al [2019] and graph clustering Miasnikof et al [2020], as well as real-world applications, including the warehouse assignment problem Sao et al [2019] and planar magnetron design Maruo et al [2020]. Bass et al Bass et al [2021] did a performance benchmark for four hybrid methods, in which the largest problem requires 10,000 binary decision variables.…”