Reverse Engineering Prefix Tables

Julien Clément (1) , Maxime Crochemore (2, 3) , Giuseppina Rindone (3)

1 Equipe AMACC - Laboratoire GREYC - UMR6072
2 DCS - Department of Computer Science
3 LIGM - Laboratoire d'Informatique Gaspard-Monge

The Prefix table of a string reports for each position the maximal length of its prefixes starting here. The Prefix table and its dual Suffix table are basic tools used in the design of the most efficient string-matching and pattern extraction algorithms. These tables can be computed in linear time independently of the alphabet size. We give an algorithmic characterisation of a Prefix table (it can be adapted to a Suffix table). Namely, the algorithm tests if an integer table of size n is the Prefix table of some word and, if successful, it constructs the lexicographically smallest string having it as a Prefix table. We show that the alphabet of the string can be bounded to log2 n letters. The overall algorithm runs in O(n) time.

Mots clés: design and analysis of algorithms; algorithms on strings; pattern matching; string matching; combinatorics on words; Prefix table; Suffix table

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

Julien Clément, Maxime Crochemore, Giuseppina Rindone. Reverse Engineering Prefix Tables. 26th International Symposium on Theoretical Aspects of Computer Science STACS 2009, Feb 2009, Freiburg, Germany. pp.289-300. ⟨inria-00359304⟩