A semidefinite programming hierarchy for covering problems in discrete geometry
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.
Cite
@article{arxiv.2312.11267,
title = {A semidefinite programming hierarchy for covering problems in discrete geometry},
author = {Cordian Riener and Jan Rolfes and Frank Vallentin},
journal= {arXiv preprint arXiv:2312.11267},
year = {2026}
}
Comments
(v2) 14 pages, referees comments incorporated, accepted in Numerical Algebra, Control and Optimization (NACO), special issue on "POP23 - Future Trends in Polynomial Optimization"