By exploring alternative approaches to combinatorial optimization, we propose the first known formal connection between clustering and set partitioning, with the goal of identifying a subclass of set partitioning problems that can be solved efficiently and with optimality guarantees through a clustering approach. We prove the equivalence between classical centroid clustering problems and a special case of set partitioning called metric k-set partitioning, we discuss k-means and regularized geometric k-medians, and we give several future extensions and applications. Finally, we discuss a case study in combinatorial optimization for carpooling.<\/p>\n","protected":false},"excerpt":{"rendered":"
By exploring alternative approaches to combinatorial optimization, we propose the first known formal connection between clustering and set partitioning, with the goal of identifying a subclass of set partitioning problems that can be solved efficiently and with optimality guarantees through a clustering approach. We prove the equivalence between classical centroid clustering problems and a special […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13561,13556],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-321836","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-research-area-artificial-intelligence","msr-locale-en_us"],"msr_publishername":"","msr_edition":"In Proceedings of the Workshop on Optimization for Machine Learning (OPT) at NIPS 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