Cover array string reconstruction

Authors:
Maxime Crochemore;Costas S. Iliopoulos;Solon P. Pissis;German Tischler
Affiliations:
Dept. of Computer Science, King's College London, London, UK and Université Paris-Est, France;Dept. of Computer Science, King's College London, London, UK and Digital Ecosystems & Business Intelligence Institute, Curtin University, Perth, WA, Australia;Dept. of Computer Science, King's College London, London, UK;Dept. of Computer Science, King's College London, London, UK
Venue:
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Year:
2010

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Abstract

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.