TY - JOUR

T1 - On pseudo-disk hypergraphs

AU - Aronov, Boris

AU - Donakonda, Anirudh

AU - Ezra, Esther

AU - Pinchasi, Rom

N1 - Funding Information:
Work on this paper by Boris Aronov has been supported by NSA MSP Grant H98230-10-1-0210, by NSF Grants CCF-08-30691, CCF-11-17336, CCF-12-18791, and CCF-15-40656, and by U.S.-Israel Binational Science Foundation grant 2014/170.Work on this paper by Anirudh Donakonda has been partially supported by NSF Grant CCF-11-17336.Work on this paper by Esther Ezra has been supported by ISF Grant 824/17, NSF under grants CAREER CCF-15-53354, CCF-11-17336, and CCF-12-16689.Work on this paper by Rom Pinchasi has been supported by ISF grant No. 409/16.
Publisher Copyright:
© 2020 Elsevier B.V.

PY - 2021/1

Y1 - 2021/1

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.

KW - Approximation algorithms

KW - Hypergraphs of finite VC dimension

KW - Minimum-weight dominating set

KW - Planar graphs

KW - Pseudo-disks

UR - http://www.scopus.com/inward/record.url?scp=85087812707&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85087812707&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2020.101687

DO - 10.1016/j.comgeo.2020.101687

M3 - Article

AN - SCOPUS:85087812707

VL - 92

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

M1 - 101687

ER -