A semidefinite programming hierarchy for packing problems in discrete geometry
Optimization and Control
2021-08-26 v3 Metric Geometry
Abstract
Packing problems in discrete geometry can be modeled as finding independent sets in infinite graphs where one is interested in independent sets which are as large as possible. For finite graphs one popular way to compute upper bounds for the maximal size of an independent set is to use Lasserre's semidefinite programming hierarchy. We generalize this approach to infinite graphs. For this we introduce topological packing graphs as an abstraction for infinite graphs coming from packing problems in discrete geometry. We show that our hierarchy converges to the independence number.
Cite
@article{arxiv.1311.3789,
title = {A semidefinite programming hierarchy for packing problems in discrete geometry},
author = {David de Laat and Frank Vallentin},
journal= {arXiv preprint arXiv:1311.3789},
year = {2021}
}
Comments
(v3) 25 pages, this revision fixes a problem in the proof of Lemma 5