On the complexity of some partition problems of a finite set of points in Euclidean space into balanced clusters
We consider some problems of partitioning a finite set of N points in d-dimension Euclidean space into two clusters balancing the value of (1) the quadratic variance normalized by a cluster size, (2) the quadratic variance, and (3) the size-weighted quadratic variance. We have proved the NP-completeness of all these problems.
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