Optimal Suffix Tree Construction with Large Alphabets

The suux 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 algorithm for building the suux tree of an n character string drawn from a constant size alphabet. In the comparison model, there is a trivial (n log n) time lower bound based on sorting, and Weiner's algorithm matches this bound trivially. Since Weiner's paper, the main open question has been how to deal with integer alphabets. 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 suux trees in linear time for integer alphabet.