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arXiv · 2312.11267

A semidefinite programming hierarchy for covering problems in discrete geometry

Cordian Riener·Jan Rolfes·Frank Vallentin
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Abstract

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.

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Cordian Riener, Jan Rolfes, Frank Vallentin. 2023-12-18. A semidefinite programming hierarchy for covering problems in discrete geometry. https://doi.org/10.3934/naco.2025015

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