Covering compact metric spaces greedily

被引：7
|
作者：
Rolfes, J. H. [1 ]
Vallentin, F. [1 ]
机构：
[1] Univ Cologne, Math Inst, Weyertal 86-90, D-50931 Cologne, Germany
来源：
ACTA MATHEMATICA HUNGARICA | 2018年 / 155卷 / 01期
关键词：
geometric covering problem; set cover; greedy algorithm;
D O I：
10.1007/s10474-018-0829-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A general greedy approach to construct coverings of compact metric spaces by metric balls is given and analyzed. The analysis is a continuous version of Chvatal's analysis of the greedy algorithm for the weighted set cover problem. The approach is demonstrated in an exemplary manner to construct efficient coverings of the n-dimensional sphere and n-dimensional Euclidean space to give short and transparent proofs of several best known bounds obtained from constructions in the literature on sphere coverings.
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页码：130 / 140
页数：11
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