Esther Ezra

Small-Size

We show the existence of

\eps

\varepsilon

-Nets for Axis-Parallel Rectangles and Boxes

-nets of size

On the performance of the ICP algorithm

O\left(\frac{1}{\varepsilon}\log\log\frac{1}{\varepsilon}\right)

On the ICP algorithm

for planar point sets and axis-parallel rectangular ranges. The same bound holds for points in the plane and “fat” triangular ranges and for point sets in

Efficient Sensor Placement for Surveillance Problems

\boldsymbol{R}^3

Output-Sensitive Construction of the Union of Triangles

and axis-parallel boxes; these are the first known nontrivial bounds for these range spaces. Our technique also yields improved bounds on the size of

Improved bounds for the union of locally fat objects in the plane

\varepsilon

A note about weak ε-nets for axis-parallel boxes in d-space

-nets in the more general context considered by Clarkson and Varadarajan. For example, we show the existence of

On the union of fat tetrahedra in three dimensions

\varepsilon