# Computing the cover array in linear time

Li, Y. and Smyth, W.F.
(2002)
*Computing the cover array in linear time.*
Algorithmica, 32
(1).
pp. 95-106.

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## Abstract

Let x denote a given nonempty string of length n = |x| . A proper substring u of x is a proper cover of x if and only if every position of x lies within an occurrence of u within x . This paper introduces an array γ = γ[1..n] called the cover array in which each element γ[i] , 1 ≤ i ≤ n , is the length of the longest proper cover of x[1..i] or zero if no such cover exists. In fact it turns out that γ describes all the covers of every prefix of x . Several interesting properties of γ are established, and a simple algorithm is presented that computes γ on-line in Θ(n) time using Θ(n) additional space. Thus the new algorithm computes for all prefixes of x information that previous cover algorithms could compute only for x itself, and does so with no increase in space or time complexity.

Item Type: | Journal Article |
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Publisher: | Springer Verlag |

URI: | http://researchrepository.murdoch.edu.au/id/eprint/27858 |

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