Symmetry breaking for suffix tree construction

Abstract

There are several serial algorithms for suffix tree construction which run in linear time, but the number of operations in the only parallel algorithm available, due to Apostolico, Iliopouloe, Landau, Schieber and Vishkin, is proportional to n log n. The algorithm is based on labeling substrings, similar to a classical serial algorithm, with the same operations bound, by Karp, Miller and Rosenberg. We show how to break symmetries that occur in the process of assigning labels using the Deterministic Coin Tossing (DCT) technique, and thereby reduce the number of labeled substrings to linear. We give several algorithms for suffix tree construction. One of them runs in 0(log2 n) parallel time and O(n) work for input strings whose characters are drawn from a constant size alphabet.