Optimal suffix tree construction with large alphabets

The suffix tree of a string is the fundamental data structure of combinatorial pattern matching. Weiner [Wei73] who introduced the data structure, gave an O(n)-time algorithm far building the suffix: tree of an n-character string Brawn from a constant size alphabet. In the comparison model, there is a trivial Omega(n log n)-time lower bound based on sorting, and Weiner's algorithm matches this bound trivially. For integer alphabets, a substantial gap remains between the known upper and lower bounds, and closing this gap is the main open question in the construction of suffix trees. There is no super-linear lower bound, and the fastest known algorithm was the O(n log n) time comparison based algorithm. We settle this open problem by closing the gap: we build suffix trees in linear fine for integer alphabet.