On pseudo-disk hypergraphs

Boris Aronov; Anirudh Donakonda; Esther Ezra; Rom Pinchasi

doi:10.1016/j.comgeo.2020.101687

On pseudo-disk hypergraphs

Boris Aronov, Anirudh Donakonda, Esther Ezra, Rom Pinchasi

Research output: Contribution to journal › Article › peer-review

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(nk³) 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 (US)
Article number	101687
Journal	Computational Geometry: Theory and Applications
Volume	92
DOIs	https://doi.org/10.1016/j.comgeo.2020.101687
State	Published - Jan 2021

Keywords

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

ASJC Scopus subject areas

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

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10.1016/j.comgeo.2020.101687

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title = "On pseudo-disk hypergraphs",

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(nk3) 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.",

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AU - Aronov, Boris

AU - Donakonda, Anirudh

AU - Ezra, Esther

AU - Pinchasi, Rom

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N2 - 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(nk3) 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.

AB - 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(nk3) 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.

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KW - Planar graphs

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On pseudo-disk hypergraphs

Abstract

Keywords

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