@inproceedings{af5ab31f52f242db9433c7d6f4301cf3,

title = "Max-Min 3-Dispersion Problems",

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.",

keywords = "Dispersion problem, Facility location",

author = "Takashi Horiyama and Nakano, {Shin ichi} and Toshiki Saitoh and Koki Suetsugu and Akira Suzuki and Ryuhei Uehara and Takeaki Uno and Kunihiro Wasa",

note = "Funding Information: Acknolwedgement. Shin-ichi Nakano was supported by JST CREST Grant Number JPMJCR1402. Takeaki Uno was supported by JST CREST Grant Number JPMJCR1401. Kunihiro Wasa was supported by JSPS KAKENHI Grant Number 19K20350 andJST CREST Grant Number JPMJCR1401. Funding Information: Acknolwedgement. Shin-ichi Nakano was supported by JST CREST Grant Number JPMJCR1402. Takeaki Uno was supported by JST CREST Grant Number JPMJCR1401. Kunihiro Wasa was supported by JSPS KAKENHI Grant Number 19K20350 and JST CREST Grant Number JPMJCR1401. Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2019.; 25th International Computing and Combinatorics Conference, COCOON 2019 ; Conference date: 29-07-2019 Through 31-07-2019",

year = "2019",

doi = "10.1007/978-3-030-26176-4_24",

language = "English",

isbn = "9783030261757",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "291--300",

editor = "Ding-Zhu Du and Zhenhua Duan and Cong Tian",

booktitle = "Computing and Combinatorics - 25th International Conference, COCOON 2019, Proceedings",

}