An Inequality for Circle Packings Proved by Semidefinite Programming

Pablo A. Parrilo, Ronen Peretz

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

A geometric inequality among three triangles, originating in circle packing problems, is introduced. In order to prove it, we reduce the original formulation to the non-negativity of a polynomial in four real indeterminates. Techniques based on sum of squares decompositions, semidefinite programming and symmetry reduction are then applied to provide an easily verifiable nonnegativity certificate.

Original languageEnglish
Pages (from-to)357-367
Number of pages11
JournalDiscrete and Computational Geometry
Volume31
Issue number3
DOIs
StatePublished - 1 Jan 2004

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