A survey of mass partitions

Abstract

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 survey we describe recent progress in the area in addition to its connections to topology, discrete geometry, and computer science.

The complexity of sharing a pizza

“…There are many other variants of mass partitions that have been studied, see e.g. [27,38] for recent surveys. In this work, we focus on the algorithmic aspects of the 2-dimensional variant of bisections with hyperplane arrangements, that is, bisections with line arrangements.…”