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In this paper we present a new semidefinite programming hierarchy forcovering problems in compact metric spaces. Over the last years, these kind ofhierarchies were developed primarily for geometric packing and for energyminimization problems; they frequently provide the best known bounds. Startingfrom a semidefinite programming hierarchy for the dominating set problem ingraph theory, we derive the new hierarchy for covering and show some of itsbasic properties: The hierarchy converges in finitely many steps, but the firstlevel collapses to the volume bound when the compact metric space ishomogeneous.

A semidefinite programming hierarchy for covering problems in discrete geometry