Abstract
A set U of unit vectors is selectively balancing if one can find two disjoint subsets U+ and U-, not both empty, such that the Euclidean distance between the sum of U+ and the sum of U- is smaller than 1. We prove that the minimum number of unit vectors that guarantee a selectively balancing set in ℝn is asymptotically 1/2nlogn.
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H. Chen is supported by the Deutsche Forschungsgemeinschaft within the Research Training Group ‘Methods for Discrete Structures’ (GRK 1408) and by NWO/DIAMANT grant number 613.009.031.
