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Efficient Algorithms for the Inverse Sort Transform
November 2007 (vol. 56 no. 11)
pp. 1564-1574
Ge Nong, IEEE
Sen Zhang, IEEE
As an important variant of the Burrows-WheelerTransform (BWT), the Sort Transform (ST) can speed up thetransformation by sorting only a portion of the matrix. However,because the currently known inverse ST algorithms need toretrieve the complete k-order contexts and use hash tables, theyare less efficient than the inverse BWT. In this paper, we proposethree fast and memory-efficient inverse ST algorithms. The firstalgorithm uses two auxiliary vectors to replace the hash tables.The algorithm achieves O(kN) time and space complexities for atext of N characters under the context order k. The second usestwo additional compact "alternate vectors" to further eliminatethe need to restore all the k-order contexts and achieve O(N)space complexity. And the third uses a "doubling technique" tofurther reduce the time complexity to O(N log2 k). The hallmarkof these three algorithms is that they can invert ST in a mannersimilar to inverting BWT in that they all make use of precalculatedauxiliary mapping vectors and require no hash tables.These unifying algorithms can also better explain the connectionbetween the BWT and the ST: their forward components can notonly be performed by the same algorithm framework, but theirrespective inverse components can also be efficiently conductedby the unifying algorithm framework proposed in the presentwork.

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Index Terms:
Burrows-Wheeler transform, inverse sort transform, limit-order contexts, algorithm design, data compression.
Ge Nong, Sen Zhang, "Efficient Algorithms for the Inverse Sort Transform," IEEE Transactions on Computers, vol. 56, no. 11, pp. 1564-1574, Nov. 2007, doi:10.1109/TC.2007.70762
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