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
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U2 - 10.1016/j.comgeo.2020.101687
DO - 10.1016/j.comgeo.2020.101687
M3 - Article
AN - SCOPUS:85087812707
SN - 0925-7721
VL - 92
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
M1 - 101687
ER -