Mass partition problems describe the partitions we can induce on a family of measures or
finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this …

In the ε-Consensus-Halving problem, we are given n probability measures v 1,…, vn on the
interval R=[0, 1], and the goal is to partition R into two parts R+ and R− using at most n cuts …

Discrete geometry on colored point sets in the plane has a long history, but this research
area has been extensively developed in the last 2 decades. In 2003, a short survey entitled …

639 Bisecting measures with hyperplane arrangements Page 1 Math. Proc. Camb. Phil. Soc.
(2020), 169, 639–647 C Cambridge Philosophical Society 2019 639 doi:10.1017/S0305004119000380 …

Assume you have a 2-dimensional pizza with $2 n $ ingredients that you want to share with
your friend. For this you are allowed to cut the pizza using several straight cuts, and then …

We study the computational complexity of computing solutions for the straight-cut and
square-cut pizza sharing problems. We show that finding an approximate solution is PPA …

Abstract The Ham-Sandwich theorem is a well-known result in geometry. It states that any d
mass distributions in R^ d R d can be simultaneously bisected by a hyperplane. The result is …

A union of an arrangement of affine hyperplanes H in R d is the real algebraic variety
associated to the principal ideal generated by the polynomial p H given as the product of the …

The classic Ham-Sandwich theorem states that for any $ d $ measurable sets in $\mathbb
{R}^ d $, there is a hyperplane that bisects them simultaneously. An extension by B\'ar\'any …

Many results about mass partitions are proved by lifting to a higher-dimensional space and
dividing the higher-dimensional space into pieces. We extend such methods to use lifting …