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AAIM

2007

Springer

2007

Springer

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.

Related Content

Added |
06 Jun 2010 |

Updated |
06 Jun 2010 |

Type |
Conference |

Year |
2007 |

Where |
AAIM |

Authors |
Yuichi Asahiro, Jesper Jansson, Eiji Miyano, Hirotaka Ono, Kouhei Zenmyo |

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