RUS  ENG
Full version
JOURNALS // Chelyabinskiy Fiziko-Matematicheskiy Zhurnal

Chelyab. Fiz.-Mat. Zh., 2019, Volume 4, Issue 1, Pages 5–17 (Mi chfmj122)

Iterative methods for approximations constructing of optimal covering for nonconvex plane sets
P. D. Lebedev

References

1. Kazakov A.L., Lebedev P.D., “Algorithms for constructing pptimal $n$-networks in metric spaces”, Automation and Remote Control, 78:7 (2017), 1290–1301  mathnet  crossref  mathscinet  zmath  elib
2. H. Melissen, “Densest packings of eleven congruent circles in a circle”, Geometriae Dedicata, 50:1 (1994), 15–25  crossref  mathscinet  zmath
3. A. Heppes, H. Melissen, “Covering a rectangle with equal circles”, Periodica Mathematica Hungarica, 34 (1997), 65–81  crossref  mathscinet  zmath
4. Kazakov A.L., Lempert A.A., Bukharov D.S., “On segmenting logistical zones for servicing continuously developed consumers”, Automation and Remote Control, 74:6 (2013), 968–977  mathnet  crossref  mathscinet  zmath
5. Desyatov V.G., Systems design for public service objects of industrial plants, Moscow Architecture Institute Publ., Moscow,, 1989, 78 pp. (In Russ.)
6. Preparata F.P., Shamos M.I., Computational Geometry: An Introduction, Springer-Verlag, New York, 1988, 420 pp.  mathscinet
7. Dem'yanov V.F., Vasil'ev L.V., Nondifferentiable Optimization, Springer-Verlag, New York, 1985, XVI+452 pp.  mathscinet  mathscinet
8. Hausdorff F., Set theory, Komkniga Publ., Moscow, 2006, 304 pp. (In Russ.)
9. Garkavi A.L., “On the existence of an optimal network and a best diameter for a set in a Banach space”, Progress in mathematical sciences, 15:2 (1960), 210–211 (In Russ.)  mathnet
10. Garkavi A.L., “On an optimal network and optimal section of a set in a normed space”, News of USSR Academy of sciences. Series mathematical, 26:1 (1962), 87–106 (In Russ.)  mathnet  zmath
11. Mestetskiy L.M., Continuous morphology of binary images: figures, skeletons, circulars, Fizmatlit Publ., Moscow, 2009, 288 pp. (In Russ.)
12. Brusov V.S., Piyavskii S.A., “A computational algorithm for optimally covering a plane region”, USSR Computational Mathematics and Mathematical Physics, 11:2 (1971), 17–27  mathnet  crossref
13. Lebedev P.D., Uspenskii A.A., Ushakov V.N., “Algorithms of the best approximation for flat sets by unions of discs”, Bulletin of Udmurt University. Mathematica. Mechanics. Computer Sciences, 2013, no. 4, 88–99 (In Russ.)  mathnet  zmath
14. Ushakov V.N., Lebedev P.D., “Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space”, Proceedings of the Steklov Institute of Mathematics, 293, no. 1, 2016, S225–S237  mathnet  crossref  crossref  mathscinet  zmath
15. Ushakov V.N., Lebedev P.D., “Algorithms of optimal set covering on the planar $\mathbb{R}^2$”, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 26:2 (2016), 258–270 (In Russ.)  mathnet  mathscinet  zmath
16. Piyavskii S.A., “On optimization of networks”, News of USSR Academy of Sciences. Technical cybernetics, 1968, no. 1, 68–80 (In Russ.)
17. Tóth L.F., Lagerungen in der Ebene auf der Kugel und im Raum, Springer, Berlin, 1953, 197 pp.  mathscinet  zmath


© Steklov Math. Inst. of RAS, 2026