Deterministic sub-linear space LCE data structures with efficient construction

Abstract

Given a string S of n symbols, a longest common extension query LCE(i, j) asks for the length of the longest common prefix of the ith and jth suffixes of S. LCE queries have several important applications in string processing, perhaps most notably to suffix sorting. Recently, Bille et al. (J. Discrete Algorithms 25:42-50, 2014, Proc. CPM 2015 described several data structures for answering LCE queries that offers a space-time trade-off between data structure size and query time. In particular, for a parameter 1 ≤ τ ≤ n, their best deterministic solution is a data structure of size O(n/τ ) which allows LCE queries to be answered in O(τ ) time. However, the construction time for all deterministic versions of their data structure is quadratic in n. In this paper, we propose a deterministic solution that achieves a similar space-time trade-off of O(τ min{log τ, log n τ }) query time using O(n/τ ) space, but significantly improve the construction time to O(nτ ).