AN O (n log n)-TIME ALGORITHM FOR THE k-CENTER PROBLEM IN TREES

被引：7

作者：

Wang, Haitao ^{[1
]}

Zhang, Jingru ^{[2
]}

机构：

[1] Utah State Univ, Dept Comp Sci, Logan, UT 84322 USA

[2] Cleveland State Univ, Dept Elect Engn & Comp Sci, Cleveland, OH 44115 USA

来源：

SIAM JOURNAL ON COMPUTING | 2021年 / 50卷 / 02期

关键词：

k-center; trees; algorithms; computational geometry; facility locations; OPTIMAL SLOPE SELECTION; P-CENTERS; COMPLEXITY; LINE;

D O I：

10.1137/18M1196522

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We consider a classical k-center problem in trees. Let T be a tree of n vertices such that every vertex has a nonnegative weight. The problem is to find k centers on the edges of T such that the maximum weighted distance from all vertices to their closest centers is minimized. Megiddo and Tamir [SIAM J. Comput., 12 (1983), pp. 751-758] gave an algorithm that can solve the problem in O(n log(2) n) time by using Cole's parametric search. Since then it has been open for over three decades whether the problem can be solved in O(n log n) time. In this paper, we present an O(n log n) time algorithm for the problem and thus settle the open problem affirmatively.

引用

页码：602 / 635

页数：34

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