DeepAI

# On Pseudo-disk Hypergraphs

Let F be a family of pseudo-disks in the plane, and P be a finite subset of F. Consider the hypergraph 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. (2013). As an application of our bound, we obtain an algorithm that computes a constant-factor approximation to the smallest _weighted_ dominating set in a collection of pseudo-disks in the plane, in expected polynomial time.

• 14 publications
• 1 publication
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02/23/2021

### On the number of hyperedges in the hypergraph of lines and pseudo-discs

Consider the hypergraph whose vertex set is a family of n lines in gener...
06/11/2018

### Plane drawings of the generalized Delaunay-graphs for pseudo-disks

We study general Delaunay-graphs, which are a natural generalizations of...
06/29/2022

### A note on the Tuza constant c_k for small k

For a hypergraph H, the transversal is a subset of vertices whose inters...
07/07/2019

### A spectral bound on hypergraph discrepancy

Let H be a t-regular hypergraph on n vertices and m edges. Let M be the ...
11/22/2021

### Novel ways of enumerating restrained dominating sets of cycles

Let G = (V, E) be a graph. A set S ⊆ V is a restrained dominating set (R...
07/18/2017

### A Note on Unconditional Subexponential-time Pseudo-deterministic Algorithms for BPP Search Problems

We show the first unconditional pseudo-determinism result for all of sea...
06/27/2019

### Smallest graphs achieving the Stinson bound

Perfect secret sharing scheme is a method of distribute a secret informa...