Abstract
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(Nlogk) and a space complexity O(N), where Nand kare 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.
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