Computing Inverse ST in Linear Complexity

Authors:
Ge Nong;Sen Zhang;Wai Hong Chan
Affiliations:
Computer Science Department, Sun Yat-Sen University, P.R.C.;Dept. of Math., Comp. Sci. and Stat., SUNY College at Oneonta, U.S.A.;Department of Mathematics, Hong Kong Baptist University, Hong Kong
Venue:
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Year:
2008

Citing 8
Cited 5

Universal Data Compression Based on the Burrows-Wheeler Transformation: Theory and Practice

IEEE Transactions on Computers
Invited Lecture: The Burrows-Wheeler Transform: Theory and Practice

MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its Applications

CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
A Fast Block-Sorting Algorithm for Lossless Data Compression

DCC '97 Proceedings of the Conference on Data Compression
Inverting the Burrows—Wheeler transform

Journal of Functional Programming
Unifying The Burrows-Wheeler and The Schindler Transforms

DCC '06 Proceedings of the Data Compression Conference
An Efficient Algorithm For The Inverse ST Problem

DCC '07 Proceedings of the 2007 Data Compression Conference
Efficient Algorithms for the Inverse Sort Transform

IEEE Transactions on Computers

Novel and Generalized Sort-Based Transform for Lossless Data Compression

SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
Extension and faster implementation of the GRP transform for lossless compression

CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Computing the inverse sort transform in linear time

ACM Transactions on Algorithms (TALG)
Revisiting bounded context block-sorting transformations

Software—Practice & Experience
Efficient indexing algorithms for approximate pattern matching in text

Proceedings of the Seventeenth Australasian Document Computing Symposium

Quantified Score

Hi-index	0.00

Visualization

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.