Maximum Polygon Packing: The CG:SHOP Challenge 2024

TL;DR

An overview of the 2024 Computational Geometry Challenge targeting the problemMaximum Polygon Packing is given, which presents significant computational challenges and are of substantial practical importance.

Abstract

We give an overview of the 2024 Computational Geometry Challenge targeting the problem \textsc{Maximum Polygon Packing}: Given a convex region $P$ in the plane, and a collection of simple polygons $Q_1, \ldots, Q_n$, each $Q_i$ with a respective value $c_i$, find a subset $S \subseteq \{1, \ldots,n\}$ and a feasible packing within $P$ of the polygons $Q_i$ (without rotation) for $i \in S$, maximizing $\sum_{i \in S} c_i$. Geometric packing problems, such as this, present significant computational challenges and are of substantial practical importance.

Figures (10)

• Figure 1: An example of a random instance.
• Figure 2: An example of a jigsaw instance.
• Figure 3: An example of an atris instance.
• Figure 4: An example of a satris instance.
• Figure 5: Pair plots of the instance metrics for the initial set of instances (top) and the final benchmark (bottom), showing the correlation between the different metrics and the distribution of the instances among them.