Graph Orientations Optimizing the Number of Light or Heavy Vertices

  • Yuichi Asahiro
  • Jesper Jansson
  • Eiji Miyano
  • Hirotaka Ono
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7422)

Abstract

This paper introduces four graph orientation problems named Maximize W -Light, Minimize W -Light, Maximize W -Heavy, and Minimize W -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.

Keywords

Planar Graph Undirected Graph Vertex Cover Maximum Clique Chordal Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yuichi Asahiro
    • 1
  • Jesper Jansson
    • 2
  • Eiji Miyano
    • 3
  • Hirotaka Ono
    • 4
  1. 1.Department of Information ScienceKyushu Sangyo UniversityHigashi-kuJapan
  2. 2.Laboratory of Mathematical Bioinformatics, Institute for Chemical ResearchKyoto UniversityUjiJapan
  3. 3.Department of Systems Design and InformaticsKyushu Institute of TechnologyIizukaJapan
  4. 4.Department of Economic EngineeringKyushu UniversityHigashi-kuJapan

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