An Inequality for Circle Packings Proved by Semidefinite Programming

Pablo A. Parrilo; Ronen Peretz

doi:10.1007/s00454-003-2880-2

An Inequality for Circle Packings Proved by Semidefinite Programming

Pablo A. Parrilo, Ronen Peretz

Department of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	357-367
Number of pages	11
Journal	Discrete and Computational Geometry
Volume	31
Issue number	3
DOIs	https://doi.org/10.1007/s00454-003-2880-2
State	Published - 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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10.1007/s00454-003-2880-2

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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.",

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AB - 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.

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An Inequality for Circle Packings Proved by Semidefinite Programming

Abstract

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