Fast scaling algorithms for M-convex function minimization with application to the resource allocation problem

Akiyoshi Shioura

doi:10.1016/S0166-218X(03)00255-5

Fast scaling algorithms for M-convex function minimization with application to the resource allocation problem

Akiyoshi Shioura

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

Abstract

M-convex functions, introduced by Murota (Adv. Math. 124 (1996) 272; Math. Prog. 83 (1998) 313), enjoy various desirable properties as "discrete convex functions." In this paper, we propose two new polynomial-time scaling algorithms for the minimization of an M-convex function. Both algorithms apply a scaling technique to a greedy algorithm for M-convex function minimization, and run as fast as the previous minimization algorithms. We also specialize our scaling algorithms for the resource allocation problem which is a special case of M-convex function minimization.

Original language	English
Pages (from-to)	303-316
Number of pages	14
Journal	Discrete Applied Mathematics
Volume	134
Issue number	1-3
DOIs	https://doi.org/10.1016/S0166-218X(03)00255-5
Publication status	Published - 2004 Jan 5
Externally published	Yes

Keywords

Base polyhedron
Convex function
Discrete optimization
Minimization
Resource allocation

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/S0166-218X(03)00255-5

Cite this

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title = "Fast scaling algorithms for M-convex function minimization with application to the resource allocation problem",

abstract = "M-convex functions, introduced by Murota (Adv. Math. 124 (1996) 272; Math. Prog. 83 (1998) 313), enjoy various desirable properties as {"}discrete convex functions.{"} In this paper, we propose two new polynomial-time scaling algorithms for the minimization of an M-convex function. Both algorithms apply a scaling technique to a greedy algorithm for M-convex function minimization, and run as fast as the previous minimization algorithms. We also specialize our scaling algorithms for the resource allocation problem which is a special case of M-convex function minimization.",

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author = "Akiyoshi Shioura",

note = "Funding Information: The author thanks Kazuo Murota for valuable comments on the manuscript, and Akihisa Tamura for stimulating discussions which lead to the second scaling algorithm. This work is supported by Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan.",

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AU - Shioura, Akiyoshi

N1 - Funding Information: The author thanks Kazuo Murota for valuable comments on the manuscript, and Akihisa Tamura for stimulating discussions which lead to the second scaling algorithm. This work is supported by Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan.

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N2 - M-convex functions, introduced by Murota (Adv. Math. 124 (1996) 272; Math. Prog. 83 (1998) 313), enjoy various desirable properties as "discrete convex functions." In this paper, we propose two new polynomial-time scaling algorithms for the minimization of an M-convex function. Both algorithms apply a scaling technique to a greedy algorithm for M-convex function minimization, and run as fast as the previous minimization algorithms. We also specialize our scaling algorithms for the resource allocation problem which is a special case of M-convex function minimization.

AB - M-convex functions, introduced by Murota (Adv. Math. 124 (1996) 272; Math. Prog. 83 (1998) 313), enjoy various desirable properties as "discrete convex functions." In this paper, we propose two new polynomial-time scaling algorithms for the minimization of an M-convex function. Both algorithms apply a scaling technique to a greedy algorithm for M-convex function minimization, and run as fast as the previous minimization algorithms. We also specialize our scaling algorithms for the resource allocation problem which is a special case of M-convex function minimization.

KW - Base polyhedron

KW - Convex function

KW - Discrete optimization

KW - Minimization

KW - Resource allocation

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Fast scaling algorithms for M-convex function minimization with application to the resource allocation problem

Abstract

Keywords

ASJC Scopus subject areas

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