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.

中文翻译：

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通过 QUBO 和数字退火进行图聚类

本文凭经验检验了使用新型专用计算机硬件解决已知难题图聚类的计算成本。我们将图聚类问题表示为簇内距离或差异最小化问题。我们将我们的问题表述为二次无约束二元优化问题，并采用新颖的计算机架构来获得数值解。我们的出发点是文献中的聚类公式。然后将该公式转换为二次无约束二元优化公式。最后，我们使用一种新颖的专用计算机架构来获得数值解。出于基准测试的目的，我们还将计算性能与使用在传统硬件上运行的商业求解器 Gurobi 获得的性能进行比较。