Graph orientations optimizing the number of light or heavy vertices

  • Authors:

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

  • Affiliations:

  • Department of Information Science, Kyushu Sangyo University, Higashi-ku, Fukuoka, Japan;Laboratory of Mathematical Bioinformatics, Institute for Chemical Research, Kyoto University, Uji, Kyoto, Japan;Department of Systems Design and Informatics, Kyushu Institute of Technology, Iizuka, Fukuoka, Japan;Department of Economic Engineering, Kyushu University, Higashi-ku, Fukuoka, Japan

  • Venue:
  • ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

Abstract

This paper introduces four graph orientation problems named MaximizeW-Light, MinimizeW-Light, MaximizeW-Heavy, and MinimizeW-Heavy, where W can be any fixed non-negative integer. In each of these problems, the input is an undirected graph G and the objective is to assign a direction to each edge in G so that the number of vertices with outdegree at most W or at least W in the resulting directed graph is maximized or minimized. We derive a number of results on the computational complexity and polynomial-time approximability of these problems for different values of W and various special classes of graphs. In particular, we show that Maximize 0-Light and Minimize 1-Heavy are equivalent to Maximum Independent Set and Minimum Vertex Cover, respectively, so by allowing the value of W to vary, we obtain a new, natural generalization of the two latter problems.