{"extern":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","language":[{"iso":"eng"}],"intvolume":"         4","title":"A hyperplane incidence problem with applications to counting distances","month":"04","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Micha","last_name":"Sharir","full_name":"Sharir, Micha"}],"date_created":"2018-12-11T12:04:00Z","publist_id":"2819","article_processing_charge":"No","abstract":[{"lang":"eng","text":"This paper proves an O(m2/3n2/3 + 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. © Springer-Verlag Berlin Heidelberg 1990."}],"date_published":"1991-04-01T00:00:00Z","citation":{"short":"H. Edelsbrunner, M. Sharir, in:, Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift, American Mathematical Society, 1991, pp. 253–263.","mla":"Edelsbrunner, Herbert, and Micha Sharir. “A Hyperplane Incidence Problem with Applications to Counting Distances.” <i>Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift</i>, vol. 4, American Mathematical Society, 1991, pp. 253–63.","chicago":"Edelsbrunner, Herbert, and Micha Sharir. “A Hyperplane Incidence Problem with Applications to Counting Distances.” In <i>Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift</i>, 4:253–63. American Mathematical Society, 1991.","ista":"Edelsbrunner H, Sharir M. 1991.A hyperplane incidence problem with applications to counting distances. In: Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 4, 253–263.","ieee":"H. Edelsbrunner and M. Sharir, “A hyperplane incidence problem with applications to counting distances,” in <i>Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift</i>, vol. 4, American Mathematical Society, 1991, pp. 253–263.","apa":"Edelsbrunner, H., &#38; Sharir, M. (1991). A hyperplane incidence problem with applications to counting distances. In <i>Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift</i> (Vol. 4, pp. 253–263). American Mathematical Society.","ama":"Edelsbrunner H, Sharir M. A hyperplane incidence problem with applications to counting distances. In: <i>Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift</i>. Vol 4. American Mathematical Society; 1991:253-263."},"volume":4,"publication":"Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift","publisher":"American Mathematical Society","status":"public","_id":"3566","type":"book_chapter","publication_status":"published","day":"01","quality_controlled":"1","oa_version":"None","date_updated":"2022-03-03T13:27:01Z","scopus_import":"1","page":"253 - 263","main_file_link":[{"url":"http://www.cs.duke.edu/~edels/Papers/1991-B-01-HyperplaneIncidence.pdf"}],"publication_identifier":{"isbn":["978-0897913850"]},"year":"1991","alternative_title":["DIMACS Series in Discrete Mathematics and Theoretical Computer Science"]}