On the complexity of the problem of choice of large clusters

The paper considers the following problem. Given a set of Euclidean vectors, find several clusters with a restriction on the maximum scatter of each cluster so that the size of the minimum cluster would be maximum. Here the scatter is the sum of squared distances from the cluster elements to its centroid. The NP-hardness of this problem is proved in the case where the dimension of the space is a part of the input. Bibliogr. 15.