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AAIM
2007
Springer

Approximation Algorithms for the Graph Orientation Minimizing the Maximum Weighted Outdegree

11 years 11 months ago
Approximation Algorithms for the Graph Orientation Minimizing the Maximum Weighted Outdegree
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.
Yuichi Asahiro, Jesper Jansson, Eiji Miyano, Hirot
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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