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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| Published in | Journal of discrete algorithms (Amsterdam, Netherlands) Vol. 34; pp. 137 - 146 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.09.2015
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1570-8667 1570-8675 |
| DOI | 10.1016/j.jda.2015.06.001 |
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| Abstract | 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(nlognlogN), which outperforms the best known polynomial-time algorithm with O(n(logN)2). |
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| AbstractList | 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(nlognlogN), which outperforms the best known polynomial-time algorithm with O(n(logN)2). |
| Author | Qin, Chao Shi, Cong Zhang, Huanan |
| Author_xml | – sequence: 1 givenname: Cong orcidid: 0000-0003-3564-3391 surname: Shi fullname: Shi, Cong email: shicong@umich.edu organization: Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI 48109, United States – sequence: 2 givenname: Huanan surname: Zhang fullname: Zhang, Huanan email: zhanghn@umich.edu organization: Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI 48109, United States – sequence: 3 givenname: Chao surname: Qin fullname: Qin, Chao email: chaoqin2019@u.northwestern.edu organization: Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208, United States |
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| Cites_doi | 10.1057/jors.1977.172 10.1287/mnsc.3.4.435 10.1287/mnsc.13.3.210 10.1016/j.ejor.2007.03.007 10.1287/opre.36.6.917 10.1287/opre.34.6.909 10.1287/mnsc.26.1.34 10.1145/322108.322114 10.1007/s10479-007-0172-6 10.1287/opre.21.2.648 10.1145/322077.322090 10.1016/j.ejor.2006.12.006 10.2307/2342192 10.1287/mnsc.10.3.441 10.1016/j.ejor.2012.10.046 10.1287/mnsc.12.11.745 10.1057/jors.1979.105 10.1287/mnsc.4.2.136 10.1109/24.55878 10.1057/jors.1974.107 |
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| Keywords | Polynomial-time algorithms Complexity analysis Nonlinear combinatorial optimization Data structure |
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| SubjectTerms | Complexity analysis Data structure Nonlinear combinatorial optimization Polynomial-time algorithms |
| Title | A faster algorithm for the resource allocation problem with convex cost functions |
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