On finding maximum-cardinality symmetric subsets

Authors:
Peter Brass
Affiliations:
Free University Berlin, Institute of Computer Science, Takustrasse 9, D-14195 Berlin, Germany
Venue:
Computational Geometry: Theory and Applications - Special issue on Discrete and computational geometry
Year:
2003

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Abstract

In this paper we study the complexity of the problem of finding a symmetric subset of maximum cardinality among n points in the plane, or in three-dimensional space, and some related problems like the largest repetitive or k-repetitive subsets. For the maximum-cardinality symmetric subset problem in the plane we obtain an algorithm of complexity O(n2.136+ε).