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On covering by translates of a set
In this paper we study the minimal number of translates of an arbitrary
subset of a group needed to cover the group, and related notions of the
efficiency of such coverings. We focus mainly on finite subsets in discrete
groups, reviewing the classical results in this area, and generalizing them to
a much broader context. For example, we show that while the worst-case
efficiency when has elements is of order , for fixed and
large, almost every -subset of any given -element group covers
with close to optimal efficiency.Comment: 41 pages; minor corrections; to appear in Random Structures and
Algorithm
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