### 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 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

*Theory of Computing 2006 - Proceedings of the 12th Computing: The Australasian Theory Symposium, CATS 2006*(Vol. 51)

**Graph Orientation Algorithms to Minimize the Maximum Outdegree.** / Asahiro, Yuichi; Miyano, Eiji; Ono, Hirotaka; Zenmyo, Kouhei.

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

*Theory of Computing 2006 - Proceedings of the 12th Computing: The Australasian Theory Symposium, CATS 2006.*vol. 51, Theory of Computing 2006 - 12th Computing: The Australasian Theory Symposium, CATS 2006, Hobart, TAS, Australia, 1/16/06.

}

TY - GEN

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.

UR - http://www.scopus.com/inward/record.url?scp=84863571152&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863571152&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84863571152

SN - 1920682333

SN - 9781920682330

VL - 51

BT - Theory of Computing 2006 - Proceedings of the 12th Computing

ER -