Covering a compact polygonal set by identical circles

Authors:
Y. G. Stoyan;V. M. Patsuk
Affiliations:
Institute for Mechanical Engineering Problems, National Ukrainian Academy of Sciences, Kharkiv, Ukraine;Institute for Mechanical Engineering Problems, National Ukrainian Academy of Sciences, Kharkiv, Ukraine
Venue:
Computational Optimization and Applications
Year:
2010

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Covering a rectangle with six and seven circles

Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization

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Abstract

The paper considers the problem of covering compact polygonal set by identical circles of minimal radius. A mathematical model of the problem based on Voronoi polygons is constructed and its characteristics are investigated. On the ground of the characteristics a modification of the Zoutendijk feasible directions method is developed to search local minima. A special approach is suggested to choose starting points. Many computational examples are given.