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Degree-Constrained Graph Orientation: Maximum Satisfaction and Minimum Violation

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Approximation and Online Algorithms (WAOA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8447))

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Abstract

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.

Supported by KAKENHI Grant Numbers 21680001, 23500020, 25104521, and 25330018 and The Hakubi Project at Kyoto University.

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Author information

Authors and Affiliations

  1. Department of Information Science, Kyushu Sangyo University, Higashi-ku, Fukuoka, 813-8503, Japan

    Yuichi Asahiro

  2. Laboratory of Mathematical Bioinformatics, Institute for Chemical Research, Kyoto University, Gokasho, Uji, Kyoto, 611-0011, Japan

    Jesper Jansson

  3. Department of Systems Design and Informatics, Kyushu Institute of Technology, Iizuka, Fukuoka, 820-8502, Japan

    Eiji Miyano

  4. Department of Economic Engineering, Kyushu University, Higashi-ku, Fukuoka, 812-8581, Japan

    Hirotaka Ono

Authors
  1. Yuichi Asahiro
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  2. Jesper Jansson
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  3. Eiji Miyano
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  4. Hirotaka Ono
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Editor information

Editors and Affiliations

  1. Computer Technology Institute and Press “Diophantus” & Department of Computer Engineering and Informatics, University of Patras, 26504, Rio, Greece

    Christos Kaklamanis

  2. University of Pittsburgh, 15260, Pittsburgh, PA, USA

    Kirk Pruhs

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Asahiro, Y., Jansson, J., Miyano, E., Ono, H. (2014). Degree-Constrained Graph Orientation: Maximum Satisfaction and Minimum Violation. In: Kaklamanis, C., Pruhs, K. (eds) Approximation and Online Algorithms. WAOA 2013. Lecture Notes in Computer Science, vol 8447. Springer, Cham. https://doi.org/10.1007/978-3-319-08001-7_3

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  • DOI: https://doi.org/10.1007/978-3-319-08001-7_3

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08000-0

  • Online ISBN: 978-3-319-08001-7

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