{"acknowledgement":"Research of the first author was supported by the National Science Foundation under grant CCR-8714565. Work of the second author was supported by Office of Naval Research Grants DCR-83-20085 and CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation, the NCRD — the Israeli National Council for Research and Development, and the Fund for Basic Research in Electronics, Computers and Communication administered by the Israeli Academy of Sciences.","article_processing_charge":"No","month":"01","date_created":"2018-12-11T12:06:45Z","citation":{"short":"H. Edelsbrunner, M. Sharir, in:, Proceedings of the International Symposium on Algorithms, Springer, 1990, pp. 419–428.","mla":"Edelsbrunner, Herbert, and Micha Sharir. “A Hyperplane Incidence Problem with Applications to Counting Distances.” <i>Proceedings of the International Symposium on Algorithms</i>, vol. 450, Springer, 1990, pp. 419–28, doi:<a href=\"https://doi.org/10.1007/3-540-52921-7_91\">10.1007/3-540-52921-7_91</a>.","ama":"Edelsbrunner H, Sharir M. A hyperplane Incidence problem with applications to counting distances. In: <i>Proceedings of the International Symposium on Algorithms</i>. Vol 450. Springer; 1990:419-428. doi:<a href=\"https://doi.org/10.1007/3-540-52921-7_91\">10.1007/3-540-52921-7_91</a>","ieee":"H. Edelsbrunner and M. Sharir, “A hyperplane Incidence problem with applications to counting distances,” in <i>Proceedings of the International Symposium on Algorithms</i>, Tokyo, Japan, 1990, vol. 450, pp. 419–428.","chicago":"Edelsbrunner, Herbert, and Micha Sharir. “A Hyperplane Incidence Problem with Applications to Counting Distances.” In <i>Proceedings of the International Symposium on Algorithms</i>, 450:419–28. Springer, 1990. <a href=\"https://doi.org/10.1007/3-540-52921-7_91\">https://doi.org/10.1007/3-540-52921-7_91</a>.","ista":"Edelsbrunner H, Sharir M. 1990. A hyperplane Incidence problem with applications to counting distances. Proceedings of the International Symposium on Algorithms. SIGAL:  Special Interest Group on Algorithms, International Symposium on Algorithms  , LNCS, vol. 450, 419–428.","apa":"Edelsbrunner, H., &#38; Sharir, M. (1990). A hyperplane Incidence problem with applications to counting distances. In <i>Proceedings of the International Symposium on Algorithms</i> (Vol. 450, pp. 419–428). Tokyo, Japan: Springer. <a href=\"https://doi.org/10.1007/3-540-52921-7_91\">https://doi.org/10.1007/3-540-52921-7_91</a>"},"status":"public","page":"419 - 428","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","extern":"1","type":"conference","date_updated":"2022-02-22T14:31:26Z","volume":450,"publication_identifier":{"isbn":["978-3-540-52921-7"]},"alternative_title":["LNCS"],"_id":"4067","doi":"10.1007/3-540-52921-7_91","conference":{"start_date":"1990-08-16","end_date":"1990-08-18","location":"Tokyo, Japan","name":"SIGAL:  Special Interest Group on Algorithms, International Symposium on Algorithms  "},"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Sharir, Micha","first_name":"Micha","last_name":"Sharir"}],"abstract":[{"text":"This paper proves an O(m 2/3 n 2/3+m+n) upper bound on the number of incidences between m points and n hyperplanes in four dimensions, assuming all points lie on one side of each hyperplane and the points and hyperplanes satisfy certain natural general position conditions. This result has application to various three-dimensional combinatorial distance problems. For example, it implies the same upper bound for the number of bichromatic minimum distance pairs in a set of m blue and n red points in three-dimensional space. This improves the best previous bound for this problem.","lang":"eng"}],"publication_status":"published","publication":"Proceedings of the International Symposium on Algorithms","day":"01","year":"1990","publisher":"Springer","date_published":"1990-01-01T00:00:00Z","publist_id":"2056","language":[{"iso":"eng"}],"intvolume":"       450","scopus_import":"1","quality_controlled":"1","title":"A hyperplane Incidence problem with applications to counting distances","main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/3-540-52921-7_91"}],"oa_version":"None"}