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arXiv · 1301.5895

When is the ball a local pessimum for covering?

Yoav Kallus
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Abstract

We consider the problem of identifying the worst point-symmetric shape for covering n-dimensional Euclidean space with lattice translates. Here we focus on the dimensions where the thinnest lattice covering with balls is known and ask whether the ball is a pessimum for covering in these dimensions compared to all point-symmetric convex shapes. We find that the ball is a local pessimum in 3 dimensions, but not so for 4 and 5 dimensions.

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Yoav Kallus. 2014-10-02. When is the ball a local pessimum for covering?. https://doi.org/10.1007/s00454-015-9690-1

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