A semidefinite programming hierarchy for covering problems in discrete geometry
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914320205479936 |
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| author | Riener, Cordian Rolfes, Jan Vallentin, Frank |
| author_facet | Riener, Cordian Rolfes, Jan Vallentin, Frank |
| contents | In this paper we present a new semidefinite programming hierarchy for covering problems in compact metric spaces. Over the last years, these kind of hierarchies were developed primarily for geometric packing and for energy minimization problems; they frequently provide the best known bounds. Starting from a semidefinite programming hierarchy for the dominating set problem in graph theory, we derive the new hierarchy for covering and show some of its basic properties: The hierarchy converges in finitely many steps, but the first level collapses to the volume bound when the compact metric space is homogeneous. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_11267 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A semidefinite programming hierarchy for covering problems in discrete geometry Riener, Cordian Rolfes, Jan Vallentin, Frank Optimization and Control Metric Geometry 90C22, 90C34, 90C48 In this paper we present a new semidefinite programming hierarchy for covering problems in compact metric spaces. Over the last years, these kind of hierarchies were developed primarily for geometric packing and for energy minimization problems; they frequently provide the best known bounds. Starting from a semidefinite programming hierarchy for the dominating set problem in graph theory, we derive the new hierarchy for covering and show some of its basic properties: The hierarchy converges in finitely many steps, but the first level collapses to the volume bound when the compact metric space is homogeneous. |
| title | A semidefinite programming hierarchy for covering problems in discrete geometry |
| topic | Optimization and Control Metric Geometry 90C22, 90C34, 90C48 |
| url | https://arxiv.org/abs/2312.11267 |