Cover array string reconstruction

Maxime Crochemore (1, 2) , Costas S. Iliopoulos (1) , Solon P. Pissis (1) , German Tischler (1)

1 Informatics
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

A proper factor u of a string y is a cover of y if every letter of y is within some occurrence of u in y. The concept generalises the notion of periods of a string. An integer array C is the minimal-cover (resp. maximal-cover) array of y if C[i] is the minimal (resp. maximal) length of covers of y[0.. i], or zero if no cover exists. In this paper, we present a constructive algorithm checking the validity of an array as a minimal-cover or maximal-cover array of some string. When the array is valid, the algorithm produces a string over an unbounded alphabet whose cover array is the input array. All algorithms run in linear time due to an interesting combinatorial property of cover arrays: the sum of important values in a cover array is bounded by twice the length of the string.

Domaines: Algorithme et structure de données [cs.DS]

Maxime Crochemore, Costas S. Iliopoulos, Solon P. Pissis, German Tischler. Cover array string reconstruction. CPM, 2010, New-York, United States. pp.251-259. ⟨hal-00742038⟩