Max-Min Dispersion on a Line

被引:3
|
作者
Araki, Tetsuya [1 ]
Nakano, Shin-ichi [2 ]
机构
[1] Tokyo Metropolitan Univ, Hachioji, Tokyo, Japan
[2] Gunma Univ, Kiryu, Gumma, Japan
关键词
Dispersion problem; Algorithm;
D O I
10.1007/978-3-030-04651-4_45
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
Given a set P of n locations on which facilities can be placed and an integer k, we want to place k facilities on some locations so that a designated objective function is maximized. The problem is called the k-dispersion problem. In this paper we give a simple O(n) time algorithm to solve the maxmin version of the k-dispersion problem if P is a set of points on a line. This is the first O(n) time algorithm to solve the max-min k-dispersion problem for the set of "unsorted" points on a line. If P is a set of sorted points on a line, and the input is given as an array in which the coordinates of the points are stored in the sorted order, then by slightly modifying the algorithm above one can solve the dispersion problem in O(log n) time. This is the first sublinear time algorithm to solve the max-min k-dispersion problem for the set of sorted points on a line.
引用
收藏
页码:672 / 678
页数:7
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