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research-article

Triangle-Based Heuristics for Area Optimal Polygonizations

Published: 25 May 2022 Publication History

Abstract

In this article, we describe an empirical study conducted on problems of Polygonizations with Optimal Area: given a set \(S\) of points in the plane, find a simple polygon with minimum (Min-Area) or maximum (Max-Area) area whose vertices are all the points of \(S\). Both problems arise in the context of pattern recognition, image reconstruction, and clustering. Higher dimensional variants play a role in object modeling, as well as optimal surface design. Both Min-Area and Max-Area are in NP-hard, and heuristics as well as exact methods have already been proposed. Our main contributions include the design and implementation of novel constructive heuristics and local search procedures to improve the solutions obtained by the former methods for the two problems.

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Cited By

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  • (2024)Exact and heuristic solutions for the prize‐collecting geometric enclosure problemInternational Transactions in Operational Research10.1111/itor.1342831:4(2093-2122)Online publication date: 13-Jan-2024
  • (2022)Area-Optimal Simple Polygonalizations: The CG Challenge 2019ACM Journal of Experimental Algorithmics10.1145/350400027(1-12)Online publication date: 4-Mar-2022

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Information & Contributors

Information

Published In

cover image ACM Journal of Experimental Algorithmics
ACM Journal of Experimental Algorithmics  Volume 27, Issue
December 2022
776 pages
ISSN:1084-6654
EISSN:1084-6654
DOI:10.1145/3505192
Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 25 May 2022
Accepted: 01 November 2021
Revised: 01 July 2021
Received: 01 January 2021
Published in JEA Volume 27

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Author Tags

  1. Polygonization
  2. computational heuristics
  3. combinatorial optimization
  4. computational geometry

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  • Research-article
  • Refereed

Funding Sources

  • Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
  • Brazilian National Council for Scientific and Technological Development (CNPq)
  • São Paulo Research Foundation (FAPESP)
  • Fund for Support to Teaching, Research and Outreach Activities (FAEPEX)

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Cited By

View all
  • (2024)Exact and heuristic solutions for the prize‐collecting geometric enclosure problemInternational Transactions in Operational Research10.1111/itor.1342831:4(2093-2122)Online publication date: 13-Jan-2024
  • (2022)Area-Optimal Simple Polygonalizations: The CG Challenge 2019ACM Journal of Experimental Algorithmics10.1145/350400027(1-12)Online publication date: 4-Mar-2022

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