Optimal Packings of Congruent Circles on a Square Flat Torus

被引：10

作者：

Musin, Oleg R. ^{[1
,2
]}

Nikitenko, Anton V. ^{[3
]}

机构：

[1] Univ Texas Rio Grande Valley, Brownsville, TX 78520 USA

[2] Russian Acad Sci, Inst Problems Informat Transmiss, Moscow, Russia

[3] IST Austria, A-3400 Klosterneuburg, Austria

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2016年 / 55卷 / 01期

基金：

美国国家科学基金会;

关键词：

Circle packing; Flat torus; Contact graph; Graph enumeration;

D O I：

10.1007/s00454-015-9742-6

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is interesting due to a practical reason-the problem of "super resolution of images." We have found optimal arrangements for , 7 and 8 circles. Surprisingly, for the case there are three different optimal arrangements. Our proof is based on a computer enumeration of toroidal irreducible contact graphs.

引用

页码：1 / 20

页数：20

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