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

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 ( n log n ) -time algorithm is presented. For the problem under the Hamming distance, we first show that it has an Ω ( n log n ) -time lo...

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Bibliographic Details
Published inJournal of computer and system sciences Vol. 75; no. 8; pp. 451 - 464
Main Authors Lin, Tzu-Chin, Kuo, Chung-Chin, Hsieh, Yong-Hsiang, Wang, Biing-Feng
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2009
Subjects
[formula omitted]-norm
Algorithms
Hamming distance
Inverse optimization
Isotonic regression
Lower bounds
Sorting
Lower bounds
l p -norm
Algorithms
Inverse optimization
Hamming distance
Isotonic regression
Sorting
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Summary: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 ( n log n ) -time algorithm is presented. For the problem under the Hamming distance, we first show that it has an Ω ( n log n ) -time lower bound in the comparison model; and then, we present an O ( n log n ) -time algorithm. Both of the presented algorithms improve the previous upper bounds from O ( n 2 ) .
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2009.04.005