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(nlog⁡n) 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.