Computing Smallest Convex Intersecting Polygons

Authors Antonios Antoniadis, Mark de Berg, Sándor Kisfaludi-Bak , Antonis Skarlatos

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Author Details

Antonios Antoniadis
  • Department for Applied Mathematics, University of Twente, Enschede, The Netherlands
Mark de Berg
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Sándor Kisfaludi-Bak
  • Department of Computer Science, Aalto University, Espoo, Finland
Antonis Skarlatos
  • Department of Computer Science, Universiät Salzburg, Austria

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Antonios Antoniadis, Mark de Berg, Sándor Kisfaludi-Bak, and Antonis Skarlatos. Computing Smallest Convex Intersecting Polygons. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 9:1-9:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


A polygon C is an intersecting polygon for a set O of objects in ℝ² if C intersects each object in O, where the polygon includes its interior. We study the problem of computing the minimum-perimeter intersecting polygon and the minimum-area convex intersecting polygon for a given set O of objects. We present an FPTAS for both problems for the case where O is a set of possibly intersecting convex polygons in the plane of total complexity n. Furthermore, we present an exact polynomial-time algorithm for the minimum-perimeter intersecting polygon for the case where O is a set of n possibly intersecting segments in the plane. So far, polynomial-time exact algorithms were only known for the minimum perimeter intersecting polygon of lines or of disjoint segments.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • convex hull
  • imprecise points
  • computational geometry


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