An Inequality for Circle Packings Proved by Semidefinite Programming

Pablo A. Parrilo, Ronen Peretz

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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
Issue number3
StatePublished - 1 Jan 2004

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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