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 in:	Journal of discrete algorithms (Amsterdam, Netherlands) Vol. 34; pp. 137 - 146
Main Authors:	Shi, Cong, Zhang, Huanan, Qin, Chao
Format:	Journal Article
Language:	English
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
ISSN:	1570-8667, 1570-8675
Online Access:	Get full text
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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