A linear-space data structure for range-LCP queries in poly-logarithmic time

Abstract 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 [ α , β ] , where 1 ≤ α β ≤ n is rlcp ( α , β ) = max ⁡ { | LCP ( T [ i , n ] , T [ j , n ] ) | | i ≠ j a n d i , j ∈ [ α , β ] } Amir et al. [2] introduced the indexing version of this problem, where the task is to build a data structure over T , so that rlcp ( α , β ) for any query range [ α , β ] can be reported efficiently. They proposed an O ( n log 1 + ϵ ⁡ n ) space structure with query time O ( log ⁡ log ⁡ n ) , and a linear space (i.e., O ( n ) words) structure with query time O ( δ log ⁡ log ⁡ n ) , where δ = β − α + 1 is the length of the input range and ϵ > 0 is an arbitrarily small constant. Later, Patil et al. [5] proposed another linear space structure with an improved query time of O ( δ log ϵ ⁡ δ ) . 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 + ϵ ⁡ n ) and construction time O ( n log ⁡ n ) .