We are happy to announce the Fifth Computational Geometry Challenge, as part of CG Week in Richardson, TX, USA, June 12-15, 2023.

As in previous years, the objective will be to compute good solutions to instances of a difficult geometric optimization problem. The specific problem chosen for the 2023 Challenge is Minimum Coverage by Convex Polygons, as follows.


Given a geometric region, P, in the plane, which may be a simple polygon or a polygon with holes. The task is to cover P with a collection, C1, …, Ck of convex polygons, each contained within P.


Minimize k, the number of convex polygons in the cover.


Optimal coverage problems have an extensive history in Computational Geometry. In fact, the well-known SoCG logo shows that an optimal solution to the Minimum Cover by rectangles may include (rotated) rectangles whose vertices are not among those of the input polygon P, even in the case that P is an orthogonal simple polygon. (See reference [1] and It is also relevant in practical contexts, such as surveillance and robot navigation.

The Minimum Cover by Convex Polygons problem is not only NP-hard [2], but was recently shown to be ∃R-complete [3], which most likely implies that it is not in the class NP.

Details of the competition (such as benchmark instances, data formats, and rules for submission and evaluation) will be announced in the coming weeks. Appropriate steps will be undertaken (e.g., by restricting the classes of feasible subsets) to ensure straightforward, automated verification of solutions.

The contributors with the most outstanding solutions will be recognized at CG Week 2023 and invited to present their results, both at the event and in the proceedings.

We are looking forward to your contributions and welcome questions and comments!


Details of the competition (such as benchmark instances, data formats, and rules for submission and evaluation) can be found on the website:


This problem was suggested by Dan Halperin, Tel Aviv University.


[1] Joseph O'Rourke. "The complexity of computing minimum convex covers for polygons," Proc. 20th Allerton Conf. Commun. Control Comput., 1982, pp. 75-84. (See )
[2] Joseph C. Culberson and Robert A. Reckhow. "Covering polygons is hard". Journal of Algorithms 17.1 (1994), pp. 2--44.
[3] Mikkel Abrahamsen. Covering polygons is even harder. FOCS 2021: 375-386.

Challenge Team

  • Sándor Fekete
  • Phillip Keldenich
  • Dominik Krupke
  • Stefan Schirra

Advisory Board

  • Bill Cook
  • Andreas Fabri
  • Dan Halperin
  • Michael Kerber
  • Philipp Kindermann
  • Joe Mitchell
  • Kevin Verbeek


A first batch of test instances will be released in late September 2022; the actual benchmark instances for the Challenge will be released in October. The contest will close in early 2023.

  • 30 September 2022: First test instances
  • 28 October 2022: Contest instances
  • 27 January 2023: Contest Closes