Deterministic sub-linear space LCE data structures with efficient construction

Given a string $S$ of $n$ symbols, a longest common extension query $\mathsf{LCE}(i,j)$ asks for the length of the longest common prefix of the $i$th and $j$th 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: 65-76) 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 $1 \leq τ\leq n$, 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 $O(τ\min\{\logτ,\log\frac{n}τ\})$ query time using $O(n/τ)$ space, but significantly improve the construction time to $O(nτ)$.