Topologically sweeping an arrangement
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
A Bibliography on Digital and Computational Convexity (1961-1988)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Searching for empty convex polygons
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
New algorithms for minimum area k-gons
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
On Convex Decompositions of Points
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Problems and Results around the Erdös-Szekeres Convex Polygon Theorem
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
MAXIMUM CLIQUE and MINIMUM CLIQUE PARTITION in Visibility Graphs
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
Computing the maximum clique in the visibility graph of a simple polygon
Journal of Discrete Algorithms
How to place efficiently guards and paintings in an art gallery
PCI'05 Proceedings of the 10th Panhellenic conference on Advances in Informatics
Operations Research Letters
Unsolved problems in visibility graphs of points, segments, and polygons
ACM Computing Surveys (CSUR)
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A largest empty convex subset of a finite set of points, S, is a maximum cardinality subset of S, that (1) are the vertices of a convex polygon, and (2) contain no other points of S interior to their convex hull. An &Ogr;(n3) time and &Ogr;(n2) space algorithm is introduced to find such subsets, where n represents the cardinality of S. Empirical results are obtained and presented. In particular, a configuration of 20 points is obtained with no empty convex hexagon, giving a partial answer to a question of Paul Erdös.