Approximation Algorithms for the Graph Orientation Minimizing the Maximum Weighted Outdegree

  • Authors:

  • Yuichi Asahiro;Jesper Jansson;Eiji Miyano;Hirotaka Ono;Kouhei Zenmyo

  • Affiliations:

  • Department of Social Information Systems, Kyushu Sangyo University, Fukuoka 813-8503, Japan;Department of Computer Science and Communication Engineering, Kyushu University, Fukuoka 812-8581, Japan;Department of Systems Innovation and Informatics, Kyushu Institute of Technology, Fukuoka 820-8502, Japan;Department of Computer Science and Communication Engineering, Kyushu University, Fukuoka 812-8581, Japan;Department of Systems Innovation and Informatics, Kyushu Institute of Technology, Fukuoka 820-8502, Japan

  • Venue:
  • AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
  • Year:
  • 2007

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Abstract

Given an undirected graph G= (V,E) and a weight function w: E茂戮驴茂戮驴+, we consider the problem of orienting all edges in Eso 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 kis 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 茂戮驴 1/k), where kis 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 茂戮驴 2/(k+ 1)) for any k茂戮驴 3, respectively, in polynomial time.