Cover Array String Reconstruction

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.

• Type: Conference
• Year: 2010
• Where: CPM
• Authors: Maxime Crochemore, Costas S. Iliopoulos, Solon P. Pissis, German Tischler
• Keywords: Cover Array, CPM 2010, Integer Array, Maximal-cover Array