{"publisher":"ACM","month":"01","type":"conference","oa_version":"None","publist_id":"2044","author":[{"first_name":"Pankaj","last_name":"Agarwal","full_name":"Agarwal, Pankaj"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Schwarzkopf","first_name":"Otfried","full_name":"Schwarzkopf, Otfried"},{"last_name":"Welzl","first_name":"Emo","full_name":"Welzl, Emo"}],"year":"1990","doi":"10.1145/98524.98567","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 &gt; 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."}],"page":"203 - 210","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","extern":"1","day":"01","scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98567"}],"_id":"4076","publication":"Proceedings of the 6th annual symposium on Computational geometry","date_created":"2018-12-11T12:06:48Z","citation":{"ama":"Agarwal P, Edelsbrunner H, Schwarzkopf O, Welzl E.  Euclidean minimum spanning trees and bichromatic closest pairs. In: <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>. ACM; 1990:203-210. doi:<a href=\"https://doi.org/10.1145/98524.98567\">10.1145/98524.98567</a>","ieee":"P. Agarwal, H. Edelsbrunner, O. Schwarzkopf, and E. Welzl, “ Euclidean minimum spanning trees and bichromatic closest pairs,” in <i>Proceedings of the 6th annual symposium on Computational geometry</i>, Berkeley, CA, United States, 1990, pp. 203–210.","mla":"Agarwal, Pankaj, et al. “ Euclidean Minimum Spanning Trees and Bichromatic Closest Pairs.” <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>, ACM, 1990, pp. 203–10, doi:<a href=\"https://doi.org/10.1145/98524.98567\">10.1145/98524.98567</a>.","chicago":"Agarwal, Pankaj, Herbert Edelsbrunner, Otfried Schwarzkopf, and Emo Welzl. “ Euclidean Minimum Spanning Trees and Bichromatic Closest Pairs.” In <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>, 203–10. ACM, 1990. <a href=\"https://doi.org/10.1145/98524.98567\">https://doi.org/10.1145/98524.98567</a>.","apa":"Agarwal, P., Edelsbrunner, H., Schwarzkopf, O., &#38; Welzl, E. (1990).  Euclidean minimum spanning trees and bichromatic closest pairs. In <i>Proceedings of the 6th annual symposium on Computational geometry</i> (pp. 203–210). Berkeley, CA, United States: ACM. <a href=\"https://doi.org/10.1145/98524.98567\">https://doi.org/10.1145/98524.98567</a>","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.","short":"P. Agarwal, H. Edelsbrunner, O. Schwarzkopf, E. Welzl, in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 203–210."},"title":" Euclidean minimum spanning trees and bichromatic closest pairs","quality_controlled":"1","date_updated":"2022-02-16T15:30:22Z","date_published":"1990-01-01T00:00:00Z","publication_identifier":{"isbn":["978-0-89791-362-1"]},"article_processing_charge":"No","conference":{"end_date":"1990-06-09","name":"SCG: Symposium on Computational Geometry","location":"Berkeley, CA, United States","start_date":"1990-06-07"},"status":"public"}