[{"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."}],"title":" Euclidean minimum spanning trees and bichromatic closest pairs","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publist_id":"2044","oa_version":"None","month":"01","author":[{"first_name":"Pankaj","last_name":"Agarwal","full_name":"Agarwal, Pankaj"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Otfried","full_name":"Schwarzkopf, Otfried","last_name":"Schwarzkopf"},{"full_name":"Welzl, Emo","last_name":"Welzl","first_name":"Emo"}],"quality_controlled":"1","extern":"1","publication_status":"published","publication":"Proceedings of the 6th annual symposium on Computational geometry","_id":"4076","date_created":"2018-12-11T12:06:48Z","status":"public","day":"01","year":"1990","language":[{"iso":"eng"}],"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","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.","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.","short":"P. Agarwal, H. Edelsbrunner, O. Schwarzkopf, E. Welzl, in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 203–210.","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"},"date_updated":"2022-02-16T15:30:22Z","scopus_import":"1","publication_identifier":{"isbn":["978-0-89791-362-1"]},"type":"conference","conference":{"end_date":"1990-06-09","location":"Berkeley, CA, United States","start_date":"1990-06-07","name":"SCG: Symposium on Computational Geometry"},"main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98567"}],"article_processing_charge":"No","page":"203 - 210","publisher":"ACM","date_published":"1990-01-01T00:00:00Z","doi":"10.1145/98524.98567"}]