Computing Inverse ST in Linear Complexity

The Sort Transform (ST) can significantly speed up the block sorting phase of the Burrows-Wheeler transform (BWT) by sorting only 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 paper, we present a novel algorithm that can compute the inverse ST in an O(N) time/space complexity, a linear result independent of k. The main idea behind the design of the linear algorithm is a set of cycle properties of k-order contexts we explored 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, leading to the proposed linear inverse ST algorithm.

• Type: Conference
• Year: 2008
• Where: CPM
• Authors: Ge Nong, Sen Zhang, Wai Hong Chan
• Keywords: Combinatorics, CPM 2008, Inverse St, K-order Contexts, Limited Order Contexts