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Covering a circular string with substrings of fixed length

Duval, A.M. and Smyth, W.F. (1996) Covering a circular string with substrings of fixed length. International Journal of Foundations of Computer Science, 7 (1). pp. 87-93.

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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| and σ is the size of the alphabet on which the strings are defined. The problem has application to DNA sequencing by hybridization using oligonucleotide probes.

Publication Type: Journal Article
Publisher: World Scientific Publishing Co.
Copyright: 1996 World Scientific Publishing Company
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