Bundling Problems in Geometric Optimization

Abstract

Arranging objects is an important and fundamental problem in many fields of industry such as packaging and logistics. Bundling is one frequently used method to arrange objects. Given $k$ geometric objects in $\mathbb{R}^d$, the bundling problem asks to find transformations of the given objects such that the size of the convex hull of the objects is minimized while they remain disjoint in their interiors. In this thesis, we study three variants of bundling problem according to the following criteria: 1) the number, 2) the dimension, 3) the complexity of the given objects. We propose efficient algorithms for these bundling problems.