### 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.

Original language | English |
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Title of host publication | Combinatorial Optimization - Second International Symposium, ISCO 2012, Revised Selected Papers |

Pages | 332-343 |

Number of pages | 12 |

Volume | 7422 LNCS |

DOIs | |

Publication status | Published - Aug 27 2012 |

Event | 2nd International Symposium on Combinatorial Optimization, ISCO 2012 - Athens, Greece Duration: Apr 19 2012 → Apr 21 2012 |

### 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 | 7422 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 2nd International Symposium on Combinatorial Optimization, ISCO 2012 |
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Country | Greece |

City | Athens |

Period | 4/19/12 → 4/21/12 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Combinatorial Optimization - Second International Symposium, ISCO 2012, Revised Selected Papers*(Vol. 7422 LNCS, pp. 332-343). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7422 LNCS). https://doi.org/10.1007/978-3-642-32147-4_30

**Graph orientations optimizing the number of light or heavy vertices.** / Asahiro, Yuichi; Jansson, Jesper; Miyano, Eiji; Ono, Hirotaka.

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

*Combinatorial Optimization - Second International Symposium, ISCO 2012, Revised Selected Papers.*vol. 7422 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7422 LNCS, pp. 332-343, 2nd International Symposium on Combinatorial Optimization, ISCO 2012, Athens, Greece, 4/19/12. https://doi.org/10.1007/978-3-642-32147-4_30

}

TY - GEN

T1 - Graph orientations optimizing the number of light or heavy vertices

AU - Asahiro, Yuichi

AU - Jansson, Jesper

AU - Miyano, Eiji

AU - Ono, Hirotaka

PY - 2012/8/27

Y1 - 2012/8/27

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84865205428&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865205428&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-32147-4_30

DO - 10.1007/978-3-642-32147-4_30

M3 - Conference contribution

AN - SCOPUS:84865205428

SN - 9783642321467

VL - 7422 LNCS

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

SP - 332

EP - 343

BT - Combinatorial Optimization - Second International Symposium, ISCO 2012, Revised Selected Papers

ER -