Computational results of a semidefinite branch-and-bound algorithm for k-cluster

•Semidefinite-based method to solve k-cluster problems to optimality.•Extensive numerical experiments and theoretical analysis.•Compared favorably with best existing methods.•For the first time, k-cluster instances on graphs with 160 nodes solved to optimality.

This computational paper presents a method to solve k-cluster problems exactly by intersecting semidefinite and polyhedral relaxations. Our algorithm uses a generic branch-and-bound method featuring an improved semidefinite bounding procedure. Extensive numerical experiments show that this algorithm outperforms the best known methods both in time and ability to solve large instances. For the first time, numerical results are reported for k-cluster problems on unstructured graphs with 160 vertices.