An Approach for LPF Table Computation

Chairungsee, Supaporn; Charuphanthuset, Thana

doi:10.1007/978-3-030-27684-3_1

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2020

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“…Methods to compute the LPF array [6,9,10,21] can be broadly classified into two categories: batch (offline) and online algorithms. For instance, in [10] the authors give two offline linear-time algorithms for computing the Longest Previous Factor (LPF) array.…”

Section: Introductionmentioning

confidence: 99%

Faster Online Computation of the Succinct Longest Previous Factor Array

Prezza

Rosone

2020

Lecture Notes in Computer Science

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We consider the problem of computing online the Longest Previous Factor array LP F [1, n] of a text T of length n. For each 1 ≤ i ≤ n, LP F [i] stores the length of the longest factor of T with at least two occurrences, one ending at i and the other at a previous position j < i. We present an improvement over the previous solution by Okanohara and Sadakane (ESA 2008): our solution uses less space (compressed instead of succinct) and runs in O(n log 2 n) time, thus being faster by a logarithmic factor. As a by-product, we also obtain the first online algorithm computing the Longest Common Suffix (LCS) array (that is, the LCP array of the reversed text) in O(n log 2 n) time and compressed space. We also observe that the LPF array can be represented succinctly in 2n bits. Our online algorithm computes directly the succinct LPF and LCS arrays.

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