{"_id":"4120","acknowledgement":"The first author was supported i~1 part by NSF grants MCS 83-03925 and the Office of Naval Research and the Defense Advanced Research Projects Agency under contract N00014-g3-K-0146 and ARPA Order No. 4786.","article_processing_charge":"No","oa_version":"Published Version","citation":{"apa":"Chazelle, B., & Edelsbrunner, H. (1985). Optimal solutions for a class of point retrieval problems. Journal of Symbolic Computation. Elsevier. https://doi.org/10.1016/S0747-7171(85)80028-6","ieee":"B. Chazelle and H. Edelsbrunner, “Optimal solutions for a class of point retrieval problems,” Journal of Symbolic Computation, vol. 1, no. 1. Elsevier, pp. 47–56, 1985.","ama":"Chazelle B, Edelsbrunner H. Optimal solutions for a class of point retrieval problems. Journal of Symbolic Computation. 1985;1(1):47-56. doi:10.1016/S0747-7171(85)80028-6","chicago":"Chazelle, Bernard, and Herbert Edelsbrunner. “Optimal Solutions for a Class of Point Retrieval Problems.” Journal of Symbolic Computation. Elsevier, 1985. https://doi.org/10.1016/S0747-7171(85)80028-6.","short":"B. Chazelle, H. Edelsbrunner, Journal of Symbolic Computation 1 (1985) 47–56.","mla":"Chazelle, Bernard, and Herbert Edelsbrunner. “Optimal Solutions for a Class of Point Retrieval Problems.” Journal of Symbolic Computation, vol. 1, no. 1, Elsevier, 1985, pp. 47–56, doi:10.1016/S0747-7171(85)80028-6.","ista":"Chazelle B, Edelsbrunner H. 1985. Optimal solutions for a class of point retrieval problems. Journal of Symbolic Computation. 1(1), 47–56."},"intvolume":" 1","publist_id":"2004","volume":1,"quality_controlled":"1","author":[{"full_name":"Chazelle, Bernard","last_name":"Chazelle","first_name":"Bernard"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"}],"publication_status":"published","date_created":"2018-12-11T12:07:03Z","status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_identifier":{"eissn":["1095-855X"],"issn":["0747-7171"]},"date_updated":"2022-01-31T09:20:18Z","month":"03","type":"journal_article","language":[{"iso":"eng"}],"title":"Optimal solutions for a class of point retrieval problems","article_type":"original","extern":"1","doi":"10.1016/S0747-7171(85)80028-6","publication":"Journal of Symbolic Computation","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0747717185800286?via%3Dihub","open_access":"1"}],"oa":1,"day":"01","issue":"1","abstract":[{"lang":"eng","text":"Let P be a set of n points in the Euclidean plane and let C be a convex figure. We study the problem of preprocessing P so that for any query point q, the points of P in C+q can be retrieved efficiently. If constant time sumces for deciding the inclusion of a point in C, we then demonstrate the existence of an optimal solution: the algorithm requires O(n) space and O(k + log n) time for a query with output size k. If C is a disk, the problem becomes the wellknown fixed-radius neighbour problem, to which we thus provide the first known optimal solution."}],"publisher":"Elsevier","page":"47 - 56","year":"1985","date_published":"1985-03-01T00:00:00Z"}