### Abstract

This paper studies the problem of orienting all edges of a weighted graph such that the maximum weighted outdegree of vertices is minimized. This problem, which has applications in the guard arrangement for example, can be shown to be AP-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, and (ii) the input graph is a tree. Then, by using those algorithms as sub-procedures, we provide a simple, combinatorial, min{w _{max}/w_{min}, (2 - ε)}-approximation algorithm for the general case, where w_{max} and w_{min} are the maximum and the minimum weights of edges, respectively, and ε is some small positive real number that depends on the input.

Original language | English |
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Pages (from-to) | 197-215 |

Number of pages | 19 |

Journal | International Journal of Foundations of Computer Science |

Volume | 18 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Computer Science (miscellaneous)

### Cite this

*International Journal of Foundations of Computer Science*,

*18*(2), 197-215. https://doi.org/10.1142/S0129054107004644