--- _id: '4120' 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.' 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 article_type: original author: - first_name: Bernard full_name: Chazelle, Bernard last_name: Chazelle - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: 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 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. ista: Chazelle B, Edelsbrunner H. 1985. Optimal solutions for a class of point retrieval problems. Journal of Symbolic Computation. 1(1), 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. short: B. Chazelle, H. Edelsbrunner, Journal of Symbolic Computation 1 (1985) 47–56. date_created: 2018-12-11T12:07:03Z date_published: 1985-03-01T00:00:00Z date_updated: 2022-01-31T09:20:18Z day: '01' doi: 10.1016/S0747-7171(85)80028-6 extern: '1' intvolume: ' 1' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://www.sciencedirect.com/science/article/pii/S0747717185800286?via%3Dihub month: '03' oa: 1 oa_version: Published Version page: 47 - 56 publication: Journal of Symbolic Computation publication_identifier: eissn: - 1095-855X issn: - 0747-7171 publication_status: published publisher: Elsevier publist_id: '2004' quality_controlled: '1' status: public title: Optimal solutions for a class of point retrieval problems type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 1 year: '1985' ...