Theory of Computing Systems

, Volume 58, Issue 1, pp 60–93 | Cite as

Degree-Constrained Graph Orientation: Maximum Satisfaction and Minimum Violation

  • Yuichi AsahiroEmail author
  • Jesper Jansson
  • Eiji Miyano
  • Hirotaka Ono


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 reference (Asahiro et al. LNCS 7422, 332–343 (2012)): 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. As shown in Asahiro et al. LNCS 7422, 332–343 (2012)).


Graph orientation Degree constraint (In)approximability Submodular function Greedy algorithm 



This work was supported by KAKENHI grant numbers 23500020, 25104521, 25330018, 26330017, and 26540005 and The Hakubi Project at Kyoto University. The authors would like to thank the anonymous reviewers for their detailed comments and suggestions that helped to improve the presentation of the paper, and Peter Floderus for pointing out an error in one of the figures.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Yuichi Asahiro
    • 1
    Email author
  • Jesper Jansson
    • 2
  • Eiji Miyano
    • 3
  • Hirotaka Ono
    • 4
  1. 1.Department of Information ScienceKyushu Sangyo UniversityFukuokaJapan
  2. 2.Laboratory of Mathematical Bioinformatics, Institute for Chemical ResearchKyoto UniversityKyotoJapan
  3. 3.Department of Systems Design and InformaticsKyushu Institute of TechnologyFukuokaJapan
  4. 4.Department of Economic EngineeringKyushu UniversityFukuokaJapan

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