Efficient algorithms for the inverse sorting problem with bound constraints under the l∞-norm and the Hamming distance

Authors:
Tzu-Chin Lin;Chung-Chin Kuo;Yong-Hsiang Hsieh;Biing-Feng Wang
Affiliations:
Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China;Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China;Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China;Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China
Venue:
Journal of Computer and System Sciences
Year:
2009

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Abstract

In this paper, we study the inverse sorting problem with bound constraints under the l"~-norm and the Hamming distance. For the problem under the l"~-norm, an O(nlogn)-time algorithm is presented. For the problem under the Hamming distance, we first show that it has an @W(nlogn)-time lower bound in the comparison model; and then, we present an O(nlogn)-time algorithm. Both of the presented algorithms improve the previous upper bounds from O(n^2).