A faster algorithm for the resource allocation problem with convex cost functions

We revisit the classical resource allocation problem with general convex objective functions, subject to an integer knapsack constraint. This class of problems is fundamental in discrete optimization and arises in a wide variety of applications. In this paper, we propose a novel polynomial-time divi...

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Bibliographic Details
Published inJournal of discrete algorithms (Amsterdam, Netherlands) Vol. 34; pp. 137 - 146
Main Authors Shi, Cong, Zhang, Huanan, Qin, Chao
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2015
Subjects
Complexity analysis
Data structure
Nonlinear combinatorial optimization
Polynomial-time algorithms
Polynomial-time algorithms
Complexity analysis
Nonlinear combinatorial optimization
Data structure
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ISSN1570-8667
1570-8675
DOI10.1016/j.jda.2015.06.001

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Summary:We revisit the classical resource allocation problem with general convex objective functions, subject to an integer knapsack constraint. This class of problems is fundamental in discrete optimization and arises in a wide variety of applications. In this paper, we propose a novel polynomial-time divide-and-conquer algorithm (called the multi-phase algorithm) and prove that it has a computational complexity of O(nlog⁡nlog⁡N), which outperforms the best known polynomial-time algorithm with O(n(log⁡N)2).
ISSN:1570-8667
1570-8675
DOI:10.1016/j.jda.2015.06.001