Empty axis-parallel boxes

09/12/2020
by   Boris Bukh, et al.
0

We show that, for every set of n points in the d-dimensional unit cube, there is an empty axis-parallel box of volume at least Ω(d/n) as n→∞ and d is fixed. In the opposite direction, we give a construction without an empty axis-parallel box of volume O(d^2log d/n). These improve on the previous best bounds of Ω(log d/n) and O(2^7d/n) respectively.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/03/2020

Geodesic Spanners for Points in ℝ^3 amid Axis-parallel Boxes

Let P be a set of n points in ℝ^3 amid a bounded number of obstacles. Wh...
research
06/21/2022

Orthogonal dissection into few rectangles

We describe a polynomial time algorithm that takes as input a polygon wi...
research
10/24/2017

A note on the dispersion of admissible lattices

In this note we show that the volume of axis-parallel boxes in R^d which...
research
09/09/2017

On the Dispersion of Sparse Grids

For any natural number d and positive number ε, we present a point set i...
research
03/14/2021

Faster Algorithms for Largest Empty Rectangles and Boxes

We revisit a classical problem in computational geometry: finding the la...
research
01/05/2022

Local Spanners Revisited

For a set of points P ⊆ℝ^2, and a family of regions , a local t-spanner ...
research
04/28/2020

The VC-Dimension of Axis-Parallel Boxes on the Torus

We show in this paper that the VC-dimension of the family of d-dimension...

Please sign up or login with your details

Forgot password? Click here to reset