Range LCP

In this paper, we define the Range LCP problem as follows. Preprocess a string S, of length n, to enable efficient solutions of the following query: Given [i,j], 0<i≤j≤n, compute max_ℓ,k[i..j]LCP(S _ℓ,S_k), where LCP(S_ℓ,S_k) is the length of the longest common prefix of the suffixes of S starting at locations ℓ and k. This is a natural generalization of the classical LCP problem. We provide algorithms with the following complexities: Preprocessing Time: O(|S|), Space: O(|S|), Query Time: O(|j-i|loglogn).Preprocessing Time: none, Space: O(|j-i|log|j-i|), Query Time: O(|j-i|log|j-i|). However, the query just gives the pairs with the longest LCP, not the LCP itself.Preprocessing Time: O(|S|^log2|S|), Space: O(|S|log1^+ε|S|) for arbitrary small constant ε, Query Time: O(loglog|S|).