Max-Min 3-Dispersion Problems

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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. 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 (forumala presented). metric, and an O(n) time algorithm to solve the 3-dispersion problem in the (forumala presented) metric. Also we give an (forumala presented) time algorithm to solve the 3-dispersion problem in the (forumala presented) metric.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 25th International Conference, COCOON 2019, Proceedings
EditorsDing-Zhu Du, Zhenhua Duan, Cong Tian
PublisherSpringer Verlag
Pages291-300
Number of pages10
ISBN (Print)9783030261757
DOIs
Publication statusPublished - 2019 Jan 1
Event25th International Computing and Combinatorics Conference, COCOON 2019 - Xi'an, China
Duration: 2019 Jul 292019 Jul 31

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11653 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference25th International Computing and Combinatorics Conference, COCOON 2019
CountryChina
CityXi'an
Period19/7/2919/7/31

Keywords

  • Dispersion problem
  • Facility location

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Horiyama, T., Nakano, S. I., Saitoh, T., Suetsugu, K., Suzuki, A., Uehara, R., Uno, T., & Wasa, K. (2019). Max-Min 3-Dispersion Problems. In D-Z. Du, Z. Duan, & C. Tian (Eds.), Computing and Combinatorics - 25th International Conference, COCOON 2019, Proceedings (pp. 291-300). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11653 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-26176-4_24