## 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 |
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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 |
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Country/Territory | 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