## Abstract

Let F be a family of pseudo-disks in the plane, and P be a finite subset of F. Consider the hyper-graph H(P,F) whose vertices are the pseudo-disks in P and the edges are all subsets of P of the form {D∈P|D∩S≠∅}, where S is a pseudo-disk in F. We give an upper bound of O(nk^{3}) for the number of edges in H(P,F) of cardinality at most k. This generalizes a result of Buzaglo et al. [4]. As an application of our bound, we obtain an algorithm that computes a constant-factor approximation to the minimum-weight dominating set in a collection of pseudo-disks in the plane, in expected polynomial time.

Original language | English |
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Article number | 101687 |

Pages (from-to) | 101687 |

Number of pages | 1 |

Journal | Computational Geometry: Theory and Applications |

Volume | 92 |

DOIs | |

State | Published - Jan 2021 |

## Keywords

- Approximation algorithms
- Hypergraphs of finite VC dimension
- Minimum-weight dominating set
- Planar graphs
- Pseudo-disks

## All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics