A Linear Space Data Structure for Range LCP Queries *

Abstract

Range LCP (longest common prefix) is an extension of the classical LCP problem and is defined as follows: Preprocess a string S[1...n] of n characters, such that whenever an interval [i, j] comes as a query, we can report max{|LCP(S_p, S_q)| | i ≤ p < q ≤ j} Here LCP(S_p, S_q) is the longest common prefix of the suffixes of S starting at locations p and q, and |LCP(S_p, S_q)| is its length. This problem was first addressed by Amir et al. [ISAAC, 2011]. They showed that the query can be answered in O(log log n) time using an O(n log^1+ɛn) space data structure for an arbitrarily small constant ɛ > 0. In an attempt to reduce the space bound, they presented a linear space data structure of O(d log log n) query time, where d = (j − i + 1). In this paper, we present a new linear space data structure with an improved query time of $O\left(\frac{\sqrt{d\log d}}{{(\log n)}^{1/2-\varepsilon }}\right)$ .