Covering a rectangle with 6 circles: a reliable mathematical programming approach

Sonia Cafieri () and Frédéric Messine ()
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Sonia Cafieri: ENAC, Université de Toulouse
Frédéric Messine: LAPLACE, ENSEEIHT-INPT, Université de Toulouse

Journal of Global Optimization, 2025, vol. 93, issue 3, No 4, 733-745

Abstract: Abstract We present a rigorous global optimization-based approach to a problem arising in discrete geometry: covering a rectangle with six identical circles while minimizing their radius. Our main contribution lies in formulating and solving this problem using mathematical programming combined with exact global optimization relying on interval-based computation. This approach not only enables the numerical proof of a theoretical result, but also certifies the accuracy of computed values by enclosing them within verified bounds, thus certifying decimal digits. This brings a strong evidence of the role of mathematical programming and rigorous exact global optimization in addressing geometric covering problems with provable precision.

Keywords: Covering; Mixed-Integer Nonlinear Optimization; Reliable Interval-based Computation; Discrete Geometry; Computer-Assisted Proof (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10898-025-01557-7

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