Degree-Constrained Graph Orientation: Maximum Satisfaction and Minimum Violation

  • Yuichi Asahiro
  • Jesper Jansson
  • Eiji Miyano
  • Hirotaka Ono
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8447)


A degree-constrained graph orientation of an undirected graph G is an assignment of a direction to each edge in G such that the outdegree of every vertex in the resulting directed graph satisfies a specified lower and/or upper bound. Such graph orientations have been studied for a long time and various characterizations of their existence are known. In this paper, we consider four related optimization problems introduced in [4]: For any fixed non-negative integer W, the problems Max W -Light, Min W -Light, Max W -Heavy, and Min W -Heavy take as input an undirected graph G and ask for an orientation of G that maximizes or minimizes the number of vertices with outdegree at most W or at least W. The problems’ computational complexities vary with W. Here, we resolve several open questions related to their polynomial-time approximability and present a number of positive and negative results.


Polynomial Time Greedy Algorithm Vertex Cover Input Graph Outerplanar 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 International Publishing Switzerland 2014

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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