Computing the inverse sort transform in linear time

The Sort Transform (ST) can significantly speed up the block sorting phase of the Burrows-Wheeler Transform (BWT) by sorting the limited order contexts. However, the best result obtained so far for the inverse ST has a time complexity O(N log k) and a space complexity O(N), where N and k are the text size and the context order of the transform, respectively. In this article, we present a novel algorithm that can compute the inverse ST for any k-order contexts in an O(N) time and space complexity, a linear result independent of k. The main idea behind the design of this linear algorithm is a set of cycle properties of k-order contexts that we explore for this work. These newly discovered cycle properties allow us to quickly compute the Longest Common Prefix (LCP) between any pair of adjacent k-order contexts that may belong to two different cycles, which eventually leads to the proposed linear-time solution. Copyright © 2011 ACM.