A Linear Space Data Structure for Range LCP Queries

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{vertical bar LCP(S-p, S-q) vertical bar vertical bar 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 vertical bar LCP(S-p, S-q)j 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+epsilon) n) space data structure for an arbitrarily small constant epsilon > 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 (root dlog d/(log n)(1/2-epsilon)).