## Abstract

We consider the Minimum Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families R where R ^{1}R^{2} is connected for every pair of rectangles R ^{1},R^{2}εR. This algorithm extends to intersection graphs of pseudo-disks. The second algorithm achieves a factor of (1.5+ε) in general rectangle families, for any fixed ε>0, and works also for the weighted variant of the problem. Both algorithms exploit the plane properties of axis-parallel rectangles in a novel way.

Original language | English |
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Pages (from-to) | 356-364 |

Number of pages | 9 |

Journal | Computational Geometry: Theory and Applications |

Volume | 44 |

Issue number | 6-7 |

DOIs | |

State | Published - Aug 2011 |

Externally published | Yes |

### Bibliographical note

Funding Information:We thank Victoria Barrientes, Kelly Benoit, Colleen Hainfeld, Melissa Walker, Mindy Sobota and Mark Sanderson for assistance in field work. Kelly Benoit first identified the tadpole's behavioral response to vocalizing male bullfrogs. We thank James and Robin Harper for permission to conduct experiments on their land. This research was supported by NIH grant NS-28565 (AMS) and an NSF Graduate Fellowship (SBH). Experimental protocols were approved by the Brown University IACUC.

### Funding

We thank Victoria Barrientes, Kelly Benoit, Colleen Hainfeld, Melissa Walker, Mindy Sobota and Mark Sanderson for assistance in field work. Kelly Benoit first identified the tadpole's behavioral response to vocalizing male bullfrogs. We thank James and Robin Harper for permission to conduct experiments on their land. This research was supported by NIH grant NS-28565 (AMS) and an NSF Graduate Fellowship (SBH). Experimental protocols were approved by the Brown University IACUC.

Funders | Funder number |
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National Science Foundation | |

National Institutes of Health | NS-28565 |

## Keywords

- Approximation algorithms
- Arrangement graphs
- Axis-parallel rectangles
- Intersection graphs
- Pseudo-disks