Covering a Circular String with Substrings of Fixed Length

@article{Duval1996CoveringAC,
  title={Covering a Circular String with Substrings of Fixed Length},
  author={Art M. Duval and William F. Smyth},
  journal={Int. J. Found. Comput. Sci.},
  year={1996},
  volume={7},
  pages={87-93}
}
A nonempty circular string C(x) of length n is said to be covered by a set Uk of strings each of fixed length k≤n iff every position in C(x) lies within an occurrence of some string u∈Uk. In this paper we consider the problem of determining the minimum cardinality of a set Uk which guarantees that every circular string C(x) of length n≥k can be covered. In particular, we show how, for any positive integer m, to choose the elements of Uk so that, for sufficiently large k, uk≈σk–m, where uk=|Uk… 
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