Computing Longest Previous Factor in linear time and applications

Maxime Crochemore (1) , Lucian Ilie (2)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 Department of Computer Science

We give two optimal linear-time algorithms for computing the Longest Previous Factor (LPF) array corresponding to a string w. For any position i in w, LPF[i] gives the length of the longest factor of w starting at position i that occurs previously in w. Several properties and applications of LPF are investigated. They include computing the Lempel-Ziv factorization of a string and detecting all repetitions (runs) in a string in linear time independently of the integer alphabet size.

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

Maxime Crochemore, Lucian Ilie. Computing Longest Previous Factor in linear time and applications. Information Processing Letters, 2008, 106 (2), pp.75-80. ⟨10.1016/j.ipl.2007.10.006⟩. ⟨hal-00619691⟩