Advertisement

Discrete & Computational Geometry

, Volume 29, Issue 1, pp 153–158 | Cite as

Finding Sets of Points without Empty Convex 6-Gons

  •  Mark Overmars

Abstract. Erdös asked whether every large enough set of points in general position in the plane contains six points that form a convex 6-gon without any points from the set in its interior. In this note we show how a set of 29 points was found that contains no empty convex 6-gon. To this end a fast incremental algorithm for finding such 6-gons was designed and implemented and a heuristic search approach was used to find promising sets. The experiments also led to two observations that might be useful in proving that large sets always contain an empty convex 6-gon.

Keywords

General Position Heuristic Search Search Approach Incremental Algorithm Empty Convex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag New York Inc. 2002

Authors and Affiliations

  •  Mark Overmars
    • 1
  1. 1.Department of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB Utrecht, The Netherlands markov@cs.uu.nlNL

Personalised recommendations