article published yes Alok Aggarwal author Herbert Edelsbrunner author 3FB178DA-F248-11E8-B48F-1D18A9856A870000-0002-9823-6833 Prabhakar Raghavan author Prasoon Tiwari author Given a sequence of n points that form the vertices of a simple polygon, we show that determining a closest pair requires OMEGA(n log n) time in the algebraic decision tree model. Together with the well-known O(n log n) upper bound for finding a closest pair, this settles an open problem of Lee and Preparata. We also extend this O(n log n) upper bound to the following problem: Given a collection of sets with a total of n points in the plane, find for each point a closest neighbor that does not belong to the same set. Elsevier1992 eng 0020-0190 1872-611910.1016/0020-0190(92)90133-G 42155 - 60 yes Aggarwal, A., Edelsbrunner, H., Raghavan, P., &#38; Tiwari, P. (1992). Optimal time bounds for some proximity problems in the plane. <i>Information Processing Letters</i>. Elsevier. <a href="https://doi.org/10.1016/0020-0190(92)90133-G">https://doi.org/10.1016/0020-0190(92)90133-G</a> Aggarwal, Alok, Herbert Edelsbrunner, Prabhakar Raghavan, and Prasoon Tiwari. “Optimal Time Bounds for Some Proximity Problems in the Plane.” <i>Information Processing Letters</i>. Elsevier, 1992. <a href="https://doi.org/10.1016/0020-0190(92)90133-G">https://doi.org/10.1016/0020-0190(92)90133-G</a>. Aggarwal, Alok, et al. “Optimal Time Bounds for Some Proximity Problems in the Plane.” <i>Information Processing Letters</i>, vol. 42, no. 1, Elsevier, 1992, pp. 55–60, doi:<a href="https://doi.org/10.1016/0020-0190(92)90133-G">10.1016/0020-0190(92)90133-G</a>. A. Aggarwal, H. Edelsbrunner, P. Raghavan, P. Tiwari, Information Processing Letters 42 (1992) 55–60. Aggarwal A, Edelsbrunner H, Raghavan P, Tiwari P. Optimal time bounds for some proximity problems in the plane. <i>Information Processing Letters</i>. 1992;42(1):55-60. doi:<a href="https://doi.org/10.1016/0020-0190(92)90133-G">10.1016/0020-0190(92)90133-G</a> A. Aggarwal, H. Edelsbrunner, P. Raghavan, and P. Tiwari, “Optimal time bounds for some proximity problems in the plane,” <i>Information Processing Letters</i>, vol. 42, no. 1. Elsevier, pp. 55–60, 1992. Aggarwal A, Edelsbrunner H, Raghavan P, Tiwari P. 1992. Optimal time bounds for some proximity problems in the plane. Information Processing Letters. 42(1), 55–60. 40482018-12-11T12:06:38Z2022-03-16T09:20:13Z