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

mathematics and information

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Citations (Scopus)

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.

Original language	English
Title of host publication	Theory of Computing 2006 - Proceedings of the 12th Computing
Subtitle of host publication	The Australasian Theory Symposium, CATS 2006
Volume	51
Publication status	Published - Dec 1 2006
Event	Theory of Computing 2006 - 12th Computing: The Australasian Theory Symposium, CATS 2006 - Hobart, TAS, Australia Duration: Jan 16 2006 → Jan 19 2006

Other

Other	Theory of Computing 2006 - 12th Computing: The Australasian Theory Symposium, CATS 2006
Country	Australia
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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Cite this

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title = "Graph Orientation Algorithms to Minimize the Maximum Outdegree",

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.",

author = "Yuichi Asahiro and Eiji Miyano and Hirotaka Ono and Kouhei Zenmyo",

year = "2006",

month = dec,

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language = "English",

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note = "Theory of Computing 2006 - 12th Computing: The Australasian Theory Symposium, CATS 2006 ; Conference date: 16-01-2006 Through 19-01-2006",

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T1 - Graph Orientation Algorithms to Minimize the Maximum Outdegree

AU - Asahiro, Yuichi

AU - Miyano, Eiji

AU - Ono, Hirotaka

AU - Zenmyo, Kouhei

PY - 2006/12/1

Y1 - 2006/12/1

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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M3 - Conference contribution

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