Faster Online Computation of the Succinct Longest Previous Factor Array

Abstract

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.

Reversed Lempel–Ziv Factorization with Suffix Trees

“…Here, Okanohara and Sadakane [32] gave a solution that works in n lg σ + O(n) bits of space and needs O(n lg 3 n) time. This time bound got recently improved to O(n lg 2 n) by Prezza and Rosone [33].…”

Non-Overlapping LZ77 Factorization and LZ78 Substring Compression Queries with Suffix Trees

“…, LPnF [1] (the algorithm of Ohlebusch and Weber [25] computes LPnF in this order). It is therefore possible to compute LPnF within O(n) bits on top of P and a compressed indexing data structures such as the FM-index [28] of the text: For that purpose, Okanohara and Sadakane [29] proposed an algorithm computing LPF and P with the FM-index in O(n lg 3 n) time, which was improved by Prezza and Rosone [30] to O(n lg 2 n) time. However, the need of P, using n lg n bits when stored in a plain array, makes an approach that transforms LPF to LPnF after computing LPF and P rather unattractive.…”