---
_id: '4076'
abstract:
- lang: eng
text: We present an algorithm to compute a Euclidean minimum spanning tree of a
given set S of n points in Ed in time O(Td(N, N) logd N), where Td(n, m) is the
time required to compute a bichromatic closest pair among n red and m blue points
in Ed. If Td(N, N) = Ω(N1+ε), for some fixed ε > 0, then the running time improves
to O(Td(N, N)). Furthermore, we describe a randomized algorithm to compute a bichromatic
closets pair in expected time O((nm log n log m)2/3+m log2 n + n log2 m) in E3,
which yields an O(N4/3log4/3 N) expected time algorithm for computing a Euclidean
minimum spanning tree of N points in E3.
article_processing_charge: No
author:
- first_name: Pankaj
full_name: Agarwal, Pankaj
last_name: Agarwal
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Otfried
full_name: Schwarzkopf, Otfried
last_name: Schwarzkopf
- first_name: Emo
full_name: Welzl, Emo
last_name: Welzl
citation:
ama: 'Agarwal P, Edelsbrunner H, Schwarzkopf O, Welzl E. Euclidean minimum spanning
trees and bichromatic closest pairs. In: Proceedings of the 6th Annual Symposium
on Computational Geometry. ACM; 1990:203-210. doi:10.1145/98524.98567'
apa: 'Agarwal, P., Edelsbrunner, H., Schwarzkopf, O., & Welzl, E. (1990). Euclidean
minimum spanning trees and bichromatic closest pairs. In Proceedings of the
6th annual symposium on Computational geometry (pp. 203–210). Berkeley, CA,
United States: ACM. https://doi.org/10.1145/98524.98567'
chicago: Agarwal, Pankaj, Herbert Edelsbrunner, Otfried Schwarzkopf, and Emo Welzl.
“ Euclidean Minimum Spanning Trees and Bichromatic Closest Pairs.” In Proceedings
of the 6th Annual Symposium on Computational Geometry, 203–10. ACM, 1990.
https://doi.org/10.1145/98524.98567.
ieee: P. Agarwal, H. Edelsbrunner, O. Schwarzkopf, and E. Welzl, “ Euclidean minimum
spanning trees and bichromatic closest pairs,” in Proceedings of the 6th annual
symposium on Computational geometry, Berkeley, CA, United States, 1990, pp.
203–210.
ista: 'Agarwal P, Edelsbrunner H, Schwarzkopf O, Welzl E. 1990. Euclidean minimum
spanning trees and bichromatic closest pairs. Proceedings of the 6th annual symposium
on Computational geometry. SCG: Symposium on Computational Geometry, 203–210.'
mla: Agarwal, Pankaj, et al. “ Euclidean Minimum Spanning Trees and Bichromatic
Closest Pairs.” Proceedings of the 6th Annual Symposium on Computational Geometry,
ACM, 1990, pp. 203–10, doi:10.1145/98524.98567.
short: P. Agarwal, H. Edelsbrunner, O. Schwarzkopf, E. Welzl, in:, Proceedings of
the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 203–210.
conference:
end_date: 1990-06-09
location: Berkeley, CA, United States
name: 'SCG: Symposium on Computational Geometry'
start_date: 1990-06-07
date_created: 2018-12-11T12:06:48Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-16T15:30:22Z
day: '01'
doi: 10.1145/98524.98567
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://dl.acm.org/doi/10.1145/98524.98567
month: '01'
oa_version: None
page: 203 - 210
publication: Proceedings of the 6th annual symposium on Computational geometry
publication_identifier:
isbn:
- 978-0-89791-362-1
publication_status: published
publisher: ACM
publist_id: '2044'
quality_controlled: '1'
scopus_import: '1'
status: public
title: ' Euclidean minimum spanning trees and bichromatic closest pairs'
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '1990'
...