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DOI: 10.4230/LIPIcs.ESA.2025.23

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

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

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

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)

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@InProceedings{picarella_et_al:LIPIcs.ESA.2025.23,
  author =	{Picarella, Gianmarco and van Kreveld, Marc and Staals, Frank and de Vries, Sjoerd},
  title =	{{Computing Largest Subsets of Points Whose Convex Hulls Have Bounded Area and Diameter}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{23:1--23:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.23},
  URN =		{urn:nbn:de:0030-drops-244919},
  doi =		{10.4230/LIPIcs.ESA.2025.23},
  annote =	{Keywords: convex polygon, dynamic programming, implementation}
}

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Documents authored by de Vries, Sjoerd

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

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