On Finding Maximum-Cardinality Symmetric Subsets

Authors:
Peter Brass
Affiliations:
-
Venue:
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Year:
2000

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Abstract

In this paper I study the complexity of the problem of finding a symmetric subset of maximum cardinality among n point in the plane, or in three-dimensional space, and some related problems like the largest repeated or k-fold repeated subsets. For the maximum-cardinality symmetric subset problem in the plane I show a connection to the maximum number of isosceles triangles among n points in the plane; if this number is denoted by I(n) this gives an algorithm of complexity O((n2 + I(n)) log n) = O(n2.136+驴 log n)