[{"extern":"1","date_updated":"2022-01-31T09:20:18Z","status":"public","article_type":"original","type":"journal_article","_id":"4120","volume":1,"issue":"1","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0747-7171"],"eissn":["1095-855X"]},"publication_status":"published","month":"03","intvolume":" 1","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0747717185800286?via%3Dihub","open_access":"1"}],"oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"title":"Optimal solutions for a class of point retrieval problems","author":[{"last_name":"Chazelle","full_name":"Chazelle, Bernard","first_name":"Bernard"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"publist_id":"2004","article_processing_charge":"No","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"ista":"Chazelle B, Edelsbrunner H. 1985. Optimal solutions for a class of point retrieval problems. Journal of Symbolic Computation. 1(1), 47–56.","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.","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.","short":"B. Chazelle, H. Edelsbrunner, Journal of Symbolic Computation 1 (1985) 47–56.","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","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","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."},"doi":"10.1016/S0747-7171(85)80028-6","date_published":"1985-03-01T00:00:00Z","date_created":"2018-12-11T12:07:03Z","page":"47 - 56","day":"01","publication":"Journal of Symbolic Computation","year":"1985","publisher":"Elsevier","quality_controlled":"1","oa":1,"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."}]