Abstract. 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.
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