TY - JOUR

T1 - Enhanced string covering

AU - Flouri, T.

AU - Iliopoulos, Costas

AU - Kociumaka, T.

AU - Pissis, S.P.

AU - Puglisi, S.J.

AU - Smyth, William

AU - Tyczyński, W.

PY - 2013

Y1 - 2013

N2 - A factor u of a string y is a cover of y if every letter of y lies within some occurrence of u in y; thus every cover u is also a border - both prefix and suffix - of y. If u is a cover of a superstring of y then u is a seed of y. Covers and seeds are two formalisations of quasiperiodicity, and there exist linear-time algorithms for computing all the covers and seeds of y. A string y covered by u thus generalises the idea of a repetition; that is, a string composed of exact concatenations of u. Even though a string is coverable somewhat more frequently than it is a repetition, still a string that can be covered by a single u is rare. As a result, seeking to find a more generally applicable and descriptive notion of cover, many articles were written on the computation of a minimum k-cover of y; that is, the minimum cardinality set of strings of length k that collectively cover y. Unfortunately, this computation turns out to be NP-hard. Therefore, in this article, we propose new, simple, easily-computed, and widely applicable notions of string covering that provide an intuitive and useful characterisation of a string: the enhanced cover; the enhanced left cover; and the enhanced left seed. © 2013 Elsevier B.V.

AB - A factor u of a string y is a cover of y if every letter of y lies within some occurrence of u in y; thus every cover u is also a border - both prefix and suffix - of y. If u is a cover of a superstring of y then u is a seed of y. Covers and seeds are two formalisations of quasiperiodicity, and there exist linear-time algorithms for computing all the covers and seeds of y. A string y covered by u thus generalises the idea of a repetition; that is, a string composed of exact concatenations of u. Even though a string is coverable somewhat more frequently than it is a repetition, still a string that can be covered by a single u is rare. As a result, seeking to find a more generally applicable and descriptive notion of cover, many articles were written on the computation of a minimum k-cover of y; that is, the minimum cardinality set of strings of length k that collectively cover y. Unfortunately, this computation turns out to be NP-hard. Therefore, in this article, we propose new, simple, easily-computed, and widely applicable notions of string covering that provide an intuitive and useful characterisation of a string: the enhanced cover; the enhanced left cover; and the enhanced left seed. © 2013 Elsevier B.V.

U2 - 10.1016/j.tcs.2013.08.013

DO - 10.1016/j.tcs.2013.08.013

M3 - Article

VL - 506

SP - 102

EP - 114

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -