论文信息 - Point Selections and Weak ε-Nets for Convex Hulls

Point Selections and Weak ε-Nets for Convex Hulls

One of our results: Let X be a finite set on the plane, 0 < e < 1. Then there exists a set F (a weak e-net) of size at most 7/e such that every convex set containing at least e|X| elements of X intersects F . Note that the size of F is independent of the size of X. 1Research supported by a United Stat es Isreal BSF grant 2On leave from the Mathematica l Institute of the Hungarian Academy of Sciences, POB 127, 1364 Budapest, Hungar y. Supported by the Program in Discrete Mathematics and its Applications at Yale , NSF grant 8901484, and Hungarian National Science Foundation grant No. 1812. 3This research was done whil e the author visited the Department of Mathematics at Massachusetts Institute of Technology. Supported in part by Hungarian National Science Foundation grant No . 1812. 4Supported in part by NSF g rants DMS–86–06225 and AFOSR–0271. Submitted to Combinatori cs, Probability, and Computation October 1991 1 2 POINT SELECTIONS AND WEAK e-NETS FOR CONVEX HULLS

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