Max-min 3-dispersion problems

Takashi Horiyama, Shin Ichi Nakano, Toshiki Saitoh, Koki Suetsugu, Akira Suzuki, Ryuhei Uehara, Takeaki Uno, Kunihiro Wasa

Research output: Contribution to journalArticlepeer-review

Abstract

Given a set P of n points on which facilities can be placed and an integer k, we want to place k facilities on some points so that the minimum distance between facilities is maximized. The problem is called the k-dispersion problem. In this paper, we consider the 3-dispersion problem when P is a set of points on a plane (2-dimensional space). Note that the 2-dispersion problem corresponds to the diameter problem. We give an O(n) time algorithm to solve the 3-dispersion problem in the L metric, and an O(n) time algorithm to solve the 3-dispersion problem in the L1 metric. Also, we give an O(n2 log n) time algorithm to solve the 3-dispersion problem in the L2 metric.

Original languageEnglish
Pages (from-to)1101-1107
Number of pages7
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE104A
Issue number9
DOIs
Publication statusPublished - 2021

Keywords

  • Algorithms
  • Dispersion problem
  • Facility location

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics

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