Graph Orientation Algorithms to Minimize the Maximum Outdegree

Yuichi Asahiro; Eiji Miyano; Hirotaka Ono; Kouhei Zenmyo

Graph Orientation Algorithms to Minimize the Maximum Outdegree

Yuichi Asahiro, Eiji Miyano, Hirotaka Ono, Kouhei Zenmyo

数理情報

研究成果: Chapter in Book/Report/Conference proceeding › Conference contribution

2 被引用数 (Scopus)

抄録

We study the problem of orienting the edges of a weighted graph such that the maximum weighted out- degree of vertices is minimized. This problem, which has applications in the guard arrangement for ex-ample, can be shown to be NP-hard generally. In this paper we first give optimal orientation algorithms which run in polynomial time for the following special cases: (i) the input is an unweighted graph, or more generally, a graph with identically weighted edges, and (ii) the input graph is a tree. Then, by using those algorithms as sub-procedures, we provide a sim-ple, combinatorial, min{wmax/wmin ; (2-ε)g-approximation algorithm for the general case, where wmax and wmin are the maximum and the minimum weights of edges, respectively, and " is some small positive real number that depends on the input.

本文言語	英語
ホスト出版物のタイトル	Theory of Computing 2006 - Proceedings of the 12th Computing
ホスト出版物のサブタイトル	The Australasian Theory Symposium, CATS 2006
巻	51
出版ステータス	出版済み - 12 1 2006
イベント	Theory of Computing 2006 - 12th Computing: The Australasian Theory Symposium, CATS 2006 - Hobart, TAS, オーストラリア継続期間: 1 16 2006 → 1 19 2006

その他

その他	Theory of Computing 2006 - 12th Computing: The Australasian Theory Symposium, CATS 2006
Country	オーストラリア
City	Hobart, TAS
Period	1/16/06 → 1/19/06

All Science Journal Classification (ASJC) codes

Computer Networks and Communications
Computer Science Applications
Hardware and Architecture
Information Systems
Software

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引用スタイル

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abstract = "We study the problem of orienting the edges of a weighted graph such that the maximum weighted out- degree of vertices is minimized. This problem, which has applications in the guard arrangement for ex-ample, can be shown to be NP-hard generally. In this paper we first give optimal orientation algorithms which run in polynomial time for the following special cases: (i) the input is an unweighted graph, or more generally, a graph with identically weighted edges, and (ii) the input graph is a tree. Then, by using those algorithms as sub-procedures, we provide a sim-ple, combinatorial, min{wmax/wmin ; (2-ε)g-approximation algorithm for the general case, where wmax and wmin are the maximum and the minimum weights of edges, respectively, and {"} is some small positive real number that depends on the input.",

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T1 - Graph Orientation Algorithms to Minimize the Maximum Outdegree

AU - Asahiro, Yuichi

AU - Miyano, Eiji

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AU - Zenmyo, Kouhei

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N2 - We study the problem of orienting the edges of a weighted graph such that the maximum weighted out- degree of vertices is minimized. This problem, which has applications in the guard arrangement for ex-ample, can be shown to be NP-hard generally. In this paper we first give optimal orientation algorithms which run in polynomial time for the following special cases: (i) the input is an unweighted graph, or more generally, a graph with identically weighted edges, and (ii) the input graph is a tree. Then, by using those algorithms as sub-procedures, we provide a sim-ple, combinatorial, min{wmax/wmin ; (2-ε)g-approximation algorithm for the general case, where wmax and wmin are the maximum and the minimum weights of edges, respectively, and " is some small positive real number that depends on the input.

AB - We study the problem of orienting the edges of a weighted graph such that the maximum weighted out- degree of vertices is minimized. This problem, which has applications in the guard arrangement for ex-ample, can be shown to be NP-hard generally. In this paper we first give optimal orientation algorithms which run in polynomial time for the following special cases: (i) the input is an unweighted graph, or more generally, a graph with identically weighted edges, and (ii) the input graph is a tree. Then, by using those algorithms as sub-procedures, we provide a sim-ple, combinatorial, min{wmax/wmin ; (2-ε)g-approximation algorithm for the general case, where wmax and wmin are the maximum and the minimum weights of edges, respectively, and " is some small positive real number that depends on the input.

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