Abstract
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 ofnpoints in the plane. Both problems are known to beNP-hard and were the subject of the 2019 Computational Geometry Challenge, which presented the quest of finding good solutions to more than 200 instances, ranging fromn= 10 all the way ton= 1, 000, 000.
Highlights
1.1 The Computational Geometry Challenge The “CG:SHOP Challenge” (Computational Geometry: Solving Hard Optimization Problems) originated as a workshop at the 2019 Computational Geometry Week (CG Week) in Portland, Oregon in June, 2019
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 plane. Both problems are known to be N P-hard and were the subject of the 2019 Computational Geometry Challenge, which presented the quest of finding good solutions to more than 200 instances, ranging from n = 10 all the way to n = 1,000,000
The goal was to conduct a computational challenge competition that focused attention on a specific hard geometric optimization problem, encouraging researchers to devise and implement solution methods that could be compared scientifically based on how well they performed on a database of instances
Summary
1.1 The Computational Geometry Challenge The “CG:SHOP Challenge” (Computational Geometry: Solving Hard Optimization Problems) originated as a workshop at the 2019 Computational Geometry Week (CG Week) in Portland, Oregon in June, 2019. The goal was to conduct a computational challenge competition that focused attention on a specific hard geometric optimization problem, encouraging researchers to devise and implement solution methods that could be compared scientifically based on how well they performed on a database of instances. A tangible outcome is a new type of special issue, presented in this volume: a series of papers focusing on algorithm engineering methods for one difficult optimization problem. In this survey, we provide background and foundations of the underlying problem and give an overview of the results and contributions
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