Some algorithms with guaranteed accuracy for 2-clustering problems with given center of one cluster

We consider the problem of 2-partitioning a finite set of points in Euclidean space minimizing the sum of squared distances between cluster elements and the corresponding cluster centers. It is assumed that the center of one of the desired clusters is the origin, while the center of the other cluster is unknown and determined as the mean value over cluster elements. In this work, we present a short survey on the results for this problem.