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Yugoslav Journal of Operations Research
2019, vol. 29, br. 1, str. 69-79
jezik rada: engleski
vrsta rada: neklasifikovan
objavljeno: 28/02/2019
doi: 10.2298/YJOR171112010L
On reserve and double covering problems for the sets with non-Euclidean metrics
(naslov ne postoji na srpskom)
aSiberian Branch of Russian Academy of Science, Matrosov Institute for System Dynamics and Control Theory, Irkutsk, Russia
bIrkutsk National Research Technical University, Irkutsk, Russia

e-adresa: lempert@icc.ru, kazakov@icc.ru, quangmungle2010@gm

Projekat

Project of the Russian Foundation for Basic Research, no. 16-06-00464.

Sažetak

(ne postoji na srpskom)
The article is devoted to Circle covering problem for a bounded set in a two-dimensional metric space with a given amount of circles. Here we focus on a more complex problem of constructing reserve and multiply coverings. Besides that, we consider the case where covering set is a multiply-connected domain. The numerical algorithms based on fundamental physical principles, established by Fermat and Huygens, are suggested and implemented. This allows us to solve the problems for the cases of non-convex sets and non-Euclidean metrics. Preliminary results of numerical experiments are presented and discussed. Calculations show the applicability of the proposed approach.

Ključne reči

Covering Problem; Fermat Principle; Huygens Principle; Wave Front; Non-Euclidean Metric; Reserve Covering; Double Covering; Computational Experiment