### 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 |
---|---|

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) |
---|---|

Volume | 7422 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

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

Country | Greece |

City | Athens |

Period | 4/19/12 → 4/21/12 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'Graph orientations optimizing the number of light or heavy vertices'. Together they form a unique fingerprint.

## 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