Lempert A.   Kazakov A.  

Congruent Circles Packing into a Multi-connected Domain with Non-Euclidean Metric and its Applications in Logistics

Reporter: Lempert A.

The optimal packing problem of equal circles (2-D spheres) in a bounded set in a two-dimensional metric space is considered. The circle packing problem is to find an arrangement in which the circles fill as large a proportion of the space as possible. In the case where the space is Euclidean this problem is well known, but the case of non-Euclidean metrics is studied much worse. However there are some applied problems, which lead us to use other special non-Euclidean metrics. For instance such statements appear in the logistics when we need to locate a
given number of commercial facilities and to maximize the overall service area. Notice, that we consider the optimal packing problem in the case, where container is a multiply-connected domain. The special algorithm based on
optical-geometric approach is suggested and implemented. The results of numerical experiment are presented and discussed. The reported study was particularly funded by RFBR according to the research projects No. 16-31-00356 and No. 16-06-00464.