Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, November 15, 2007, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Lorenz Klaus

k-Sets in Three Dimensions

Given a finite set P of points in the d-dimensional Euclidean space, a k-set of P is a subset Q of P of size k, such that Q can be linearly separated from the remaining points of P. There has been a lot of effort among many researchers to give good upper and lower bounds on the maximum number of k-sets but the question is still widely open even in low dimensions (2 - 4). The paper presents the currently best upper bound of O(nk^(3/2)) on the maximum number of k-sets of n points in 3 dimensions.

Paper by M. Sharir, S. Smorodinsky, G. Tardos, An Improved Bound for k-Sets in Three Dimensions, Discrete Comput. Geom. 26 (2001), 195-204.

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