### Abstract

Given an undirected graph G = (V, E) and a weight function w : E → ℤ^{+}, we consider the problem of orienting all edges in E so that the maximum weighted outdegree among all vertices is minimized. In this paper (1) we prove that the problem is strongly NP-hard if all edge weights belong to the set {1 ,k}, where k is any integer greater than or equal to 2, and that there exists no pseudo-polynomial time approximation algorithm for this problem whose approximation ratio is smaller than (1 + 1/k) unless P=NP; (2) we present a polynomial time algorithm that approximates the general version of the problem within a factor of (2 - 1/k), where k is the maximum weight of an edge in G; (3) we show how to approximate the special case in which all edge weights belong to {1, k} within a factor of 3/2 for k = 2 (note that this matches the inapproximability bound above), and (2 - 2/(k + 1)) for any k ≥ 3, respectively, in polynomial time.

Original language | English |
---|---|

Title of host publication | Algorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings |

Pages | 167-177 |

Number of pages | 11 |

Volume | 4508 LNCS |

Publication status | Published - 2007 |

Event | 3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007 - Portland, OR, United States Duration: Jun 6 2007 → Jun 8 2007 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 4508 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007 |
---|---|

Country | United States |

City | Portland, OR |

Period | 6/6/07 → 6/8/07 |

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

## Fingerprint Dive into the research topics of 'Approximation algorithms for the graph orientation minimizing the maximum weighted outdegree'. Together they form a unique fingerprint.

## Cite this

*Algorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings*(Vol. 4508 LNCS, pp. 167-177). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4508 LNCS).