Tight Lower Bounds for the Longest Common Extension Problem

The longest common extension problem is to preprocess a given string of length n into a data structure that uses S(n) bits on top of the input and answers in T (n) time the queries LCE (i, j) computing the length of the longest string that occurs at both positions i and j in the input. We prove that the trade-off S(n)T (n) = Ω(n logn) holds in the non-uniform cell-probe model provided that the input string is read-only, each letter occupies a separate memory cell, S(n) = Ω(n), and the size of the input alphabet is at least 28⌈S(n)/n⌉. It is known that this trade-off is tight.