article published yes Bernard Chazelle author Herbert Edelsbrunner author 3FB178DA-F248-11E8-B48F-1D18A9856A870000-0002-9823-6833 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. Elsevier1985 eng 0747-7171 1095-855X10.1016/S0747-7171(85)80028-6 1147 - 56 yes B. Chazelle, H. Edelsbrunner, Journal of Symbolic Computation 1 (1985) 47–56. Chazelle, Bernard, and Herbert Edelsbrunner. “Optimal Solutions for a Class of Point Retrieval Problems.” <i>Journal of Symbolic Computation</i>, vol. 1, no. 1, Elsevier, 1985, pp. 47–56, doi:<a href="https://doi.org/10.1016/S0747-7171(85)80028-6">10.1016/S0747-7171(85)80028-6</a>. Chazelle B, Edelsbrunner H. 1985. Optimal solutions for a class of point retrieval problems. Journal of Symbolic Computation. 1(1), 47–56. B. Chazelle and H. Edelsbrunner, “Optimal solutions for a class of point retrieval problems,” <i>Journal of Symbolic Computation</i>, vol. 1, no. 1. Elsevier, pp. 47–56, 1985. Chazelle B, Edelsbrunner H. Optimal solutions for a class of point retrieval problems. <i>Journal of Symbolic Computation</i>. 1985;1(1):47-56. doi:<a href="https://doi.org/10.1016/S0747-7171(85)80028-6">10.1016/S0747-7171(85)80028-6</a> Chazelle, Bernard, and Herbert Edelsbrunner. “Optimal Solutions for a Class of Point Retrieval Problems.” <i>Journal of Symbolic Computation</i>. Elsevier, 1985. <a href="https://doi.org/10.1016/S0747-7171(85)80028-6">https://doi.org/10.1016/S0747-7171(85)80028-6</a>. Chazelle, B., &#38; Edelsbrunner, H. (1985). Optimal solutions for a class of point retrieval problems. <i>Journal of Symbolic Computation</i>. Elsevier. <a href="https://doi.org/10.1016/S0747-7171(85)80028-6">https://doi.org/10.1016/S0747-7171(85)80028-6</a> 41202018-12-11T12:07:03Z2022-01-31T09:20:18Z