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 …

We give an overview of theoretical and practical aspects of finding a simple polygon of
minimum (Min-Area) or maximum (Max-Area) possible area for a given set of n points in the …

The aim of the “CG: SHOP Challenge 2019” was to generate optimal area polygonizations of
a planar point set. We describe here the algorithm that won the challenge. It is a two-phase …

In this paper, we describe exact methods to solve two problems: given a set S of n points in
the plane, find a simple polygon whose set of vertices is precisely S and has minimum (Min …

In this article, we present our heuristic solutions to the problems of finding the maximum and
minimum area polygons with a given set of vertices. Our solutions are based mostly on two …

We study a variety of sparsification approaches for a spectrum of geometric optimization
problems related to tour problems, such as the Angular TSP, the Minimum Perimeter …

In this paper, we propose modifications of some known efficient algorithms for solving the
problem of MAP (finding a simple polygon of minimum area). We propose an algorithm that …

Minimum area polygonization is a well-known NP-complete problem in computational
geometry. It is the problem of finding a simple polygon with minimum area for a given set of …

A polygon is simple if it is a closed chain of straight line segments that do not self-intersect.
Given a finite set P of input points in the Euclidean plane, the search for a simple polygon …

Results Instances We generated a set of 50 uniformly random instances: 10 per value of n=
10, 15, 20, 25, 30. We use “base” to refer to the above formulation;“simple” and “gen” …