Computing Longest Previous Factor in linear time and applications

• Published in: Information processing letters Vol. 106; no. 2; pp. 75 - 80
• Main Authors: Crochemore, Maxime, Ilie, Lucian
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.04.2008; Elsevier Science; Elsevier Sequoia S.A; Elsevier
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Analysis of algorithms; Applied sciences; Combinatorics; Combinatorics. Ordered structures; Computer Science; Computer science; control theory; systems; Data Structures and Algorithms; Design of algorithms; Designs and configurations; Exact sciences and technology; Information processing; Lempel–Ziv factorization; Longest common prefix; Longest previous factor; Mathematics; Miscellaneous; Repetitions; Runs; Sciences and techniques of general use; Strings; Studies; Suffix array; Theoretical computing; Design of algorithms; Longest previous factor; Repetitions; Lempel–Ziv factorization; Analysis of algorithms; Strings; Suffix array; Longest common prefix; Runs; Alphabet; Computer theory; Optimal algorithm; Linear time; Computing; Factorization; Integer; Array; Suffix; Information processing; Lempel-Ziv factorization; Application; Algorithm analysis; Repetition
• ISSN: 0020-0190; 1872-6119
• DOI: 10.1016/j.ipl.2007.10.006

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.