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- W2548382023 abstract "LetD be a set of n pairwise disjoint unit balls in R d and P the set of their center points. A hyperplane H is an m-separator for D if each closed halfspace bounded by H contains at least m points from P. This generalizes the notion of halving hyperplanes, which correspond to n=2-separators. The analogous notion for point sets has been well studied. Separators have various applications, for instance, in divide-andconquer schemes. In such a scheme any ball that is intersected by the separating hyperplane may still interact with both sides of the partition. Therefore it is desirable that the separating hyperplane intersects a small number of balls only. We present two deterministic algorithms to bisect or approximately bisect a given set of disjoint unit balls by a hyperplane: Firstly, we present a simple linear-time algorithm to construct ann -separator for balls in R d , for any 0 < < 1=2, that intersects at mostcn (d 1)=d balls, for some constantc that depends on d and . The number of intersected balls is best possible up to the constant c. Secondly, we present a near-linear time algorithm to construct an (n=2 o(n))-separator in R d that intersects o(n) balls." @default.
- W2548382023 created "2016-11-11" @default.
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- W2548382023 date "2014-01-01" @default.
- W2548382023 modified "2023-09-29" @default.
- W2548382023 title "Separating Balls with a Hyperplane" @default.
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