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Multiple covering of a closed set on a plane with non-Euclidean metrics

Авторы: Lempert A., Le Q.

Журнал: IFAC-PapersOnLine

Том: 51

Номер: 32

Год: 2018

Отчётный год: 2018

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Аннотация: The article is devoted to multiple circle covering problem for a bounded set in a two-dimensional metric space with a given amount of circles. Such statements arise in the construction of global navigation systems like GPS and Glonass. A similar problem appears in infrastructure logistics if there is a main servicing system and it is necessary to create a duplicate system to support service in the case of failure of one or more nodes. To solve this problem, we propose a computational algorithm based on a combination of the optical -geometric approach due to Fermat and Huygens principles and Voronoi diagram. A key feature of the algorithm is the ability to deal with non-Euclidean metrics. Numerical results and a comparison with known approaches are presented and discussed.

Индексируется WOS: 1

Индексируется Scopus: 1

Индексируется РИНЦ: 1

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