Abstract: We present a method to obtain upper bounds on covering numbers. As applications of this method, we reprove and generalize results of Rogers on economically covering Euclidean $n$-space with translates of a convex body, or more generally, any measurable set. We obtain a bound for the density of covering the $n$-sphere by rotated copies of a spherically convex set (or, any measurable set). Using the same method, we sharpen an estimate by Artstein--Avidan and Slomka on covering a bounded set by translates of another. The main novelty of our method...
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Topics: 
Algorithm
Artificial intelligence