A Linear-Space Data Structure For Range-Lcp Queries In Poly-Logarithmic Time

Let T[1, n] be a text of length n and T[i, n] be the suffix starting at position i. Also, for any two strings X and Y, let LCP(X, Y) denote their longest common prefix. The range-LCP of T w.r.t. a range [alpha, beta], where 1 <= alpha < beta <= n isrlcp(alpha, beta) = max{vertical bar LCP(T[i, n], T[j, n])vertical bar vertical bar i not equal j and i, j is an element of [alpha, beta]}Amir et al. [ISAAC 2011] introduced the indexing version of this problem, where the task is to build a data structure over inverted perpendicular, so that rlcp(alpha, beta) for any query range [alpha, beta] can be reported efficiently. They proposed an O(n log(1+epsilon) n) space structure with query time O(log log n), and a linear space (i.e., O(n) words) structure with query time O(delta log log n), where delta = beta - alpha + 1 is the length of the input range and epsilon > 0 is an arbitrarily small constant. Later, Patil et al. [SPIRE 2013] proposed another linear space structure with an improved query time of O(root delta log(epsilon) delta). This poses an interesting question, whether it is possible to answer rlcp(. , .) queries in poly-logarithmic time using a linear space data structure. In this paper, we settle this question by presenting an O(n) space data structure with query time O(log(1+epsilon) n) and construction time O(n log n).