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Computing Largest Subsets of Points Whose Convex Hulls Have Bounded Area and Diameter

Authors Gianmarco Picarella , Marc van Kreveld , Frank Staals , Sjoerd de Vries

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ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • convex polygon
  • dynamic programming
  • implementation

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Abstract

We study the problem of computing a convex region with bounded area and diameter that contains the maximum number of points from a given point set P. We show that this problem can be solved in O(n⁶k) time and O(n³k) space, where n is the size of P and k is the maximum number of points in the found region. We experimentally compare this new algorithm with an existing algorithm that does the same but without the diameter constraint, which runs in O(n³k) time. For the new algorithm, we use different diameters. We use both synthetic data and data from an application in cancer detection, which motivated our research.

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Gianmarco Picarella, Marc van Kreveld, Frank Staals, and Sjoerd de Vries. Computing Largest Subsets of Points Whose Convex Hulls Have Bounded Area and Diameter. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 23:1-23:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.23

Author Details

Gianmarco Picarella
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Marc van Kreveld
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Frank Staals
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Sjoerd de Vries
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
  • Department of Digital Health, University Medical Center Utrecht, The Netherlands

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References

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