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On covering by translates of a set

Abstract:

In this paper we study the minimal number of translates of an arbitrary subset $S$ of a group $G$ 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 $S$ has $k$ elements is of order $1/\log k$, for $k$ fixed and $n$ large, almost every $k$-subset of an...

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Publication status:
Published

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Publisher copy:
10.1002/rsa.20346

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Journal:
Random Structures and Algorithms 38 (2011), 33--67
Volume:
38
Issue:
1-2
Pages:
33-67
Publication date:
2009-10-20
DOI:
EISSN:
1098-2418
ISSN:
1042-9832
URN:
uuid:55b6385b-e9d8-4c2c-8316-8b40c8d13a5f
Source identifiers:
112612
Local pid:
pubs:112612
Language:
English
Keywords:

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