### 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.

Original language | English |
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Title of host publication | Approximation and Online Algorithms - 11th International Workshop, WAOA 2013, Revised Selected Papers |

Publisher | Springer Verlag |

Pages | 24-36 |

Number of pages | 13 |

ISBN (Print) | 9783319080000 |

DOIs | |

Publication status | Published - Jan 1 2014 |

Event | 11th International Workshop on Approximation and Online Algorithms, WAOA 2013 - Sophia Antipolis, France Duration: Sep 5 2013 → Sep 6 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8447 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 11th International Workshop on Approximation and Online Algorithms, WAOA 2013 |
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Country | France |

City | Sophia Antipolis |

Period | 9/5/13 → 9/6/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Approximation and Online Algorithms - 11th International Workshop, WAOA 2013, Revised Selected Papers*(pp. 24-36). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8447 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-08001-7_3

**Degree-constrained graph orientation : Maximum satisfaction and minimum violation.** / Asahiro, Yuichi; Jansson, Jesper; Miyano, Eiji; Ono, Hirotaka.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Approximation and Online Algorithms - 11th International Workshop, WAOA 2013, Revised Selected Papers.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8447 LNCS, Springer Verlag, pp. 24-36, 11th International Workshop on Approximation and Online Algorithms, WAOA 2013, Sophia Antipolis, France, 9/5/13. https://doi.org/10.1007/978-3-319-08001-7_3

}

TY - GEN

T1 - Degree-constrained graph orientation

T2 - Maximum satisfaction and minimum violation

AU - Asahiro, Yuichi

AU - Jansson, Jesper

AU - Miyano, Eiji

AU - Ono, Hirotaka

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84903631659&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903631659&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-08001-7_3

DO - 10.1007/978-3-319-08001-7_3

M3 - Conference contribution

AN - SCOPUS:84903631659

SN - 9783319080000

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 24

EP - 36

BT - Approximation and Online Algorithms - 11th International Workshop, WAOA 2013, Revised Selected Papers

PB - Springer Verlag

ER -