### 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 problem, the input is an undirected, unweighted graph G and the objective is to assign a direction to every 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. 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 are derived. In particular, it is shown that MAXIMIZE 0-LIGHT and MINIMIZE 1-HEAVY are identical to MAXIMUM INDEPENDENT SET and MINIMUM VERTEX COVER, respectively, so by allowing the value of W to vary, we obtain a new generalization of the two latter problems.

Original language | English |
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Pages (from-to) | 441-465 |

Number of pages | 25 |

Journal | Journal of Graph Algorithms and Applications |

Volume | 19 |

Issue number | 1 |

DOIs | |

Publication status | Published - Aug 1 2015 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)
- Computer Science Applications
- Geometry and Topology
- Computational Theory and Mathematics

### Cite this

*Journal of Graph Algorithms and Applications*,

*19*(1), 441-465. https://doi.org/10.7155/jgaa.00371

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

Research output: Contribution to journal › Article

*Journal of Graph Algorithms and Applications*, vol. 19, no. 1, pp. 441-465. https://doi.org/10.7155/jgaa.00371

}

TY - JOUR

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

AU - Asahiro, Yuichi

AU - Jansson, Jesper

AU - Miyano, Eiji

AU - Ono, Hirotaka

PY - 2015/8/1

Y1 - 2015/8/1

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 problem, the input is an undirected, unweighted graph G and the objective is to assign a direction to every 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. 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 are derived. In particular, it is shown that MAXIMIZE 0-LIGHT and MINIMIZE 1-HEAVY are identical to MAXIMUM INDEPENDENT SET and MINIMUM VERTEX COVER, respectively, so by allowing the value of W to vary, we obtain a new 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 problem, the input is an undirected, unweighted graph G and the objective is to assign a direction to every 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. 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 are derived. In particular, it is shown that MAXIMIZE 0-LIGHT and MINIMIZE 1-HEAVY are identical to MAXIMUM INDEPENDENT SET and MINIMUM VERTEX COVER, respectively, so by allowing the value of W to vary, we obtain a new generalization of the two latter problems.

UR - http://www.scopus.com/inward/record.url?scp=84951278348&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951278348&partnerID=8YFLogxK

U2 - 10.7155/jgaa.00371

DO - 10.7155/jgaa.00371

M3 - Article

AN - SCOPUS:84951278348

VL - 19

SP - 441

EP - 465

JO - Journal of Graph Algorithms and Applications

JF - Journal of Graph Algorithms and Applications

SN - 1526-1719

IS - 1

ER -