Abstract:
We give polynomial time approximation schemes for the problem of partitioning an input set of n points into a fixed number k of clusters so as to minimize the sum over all clusters of the total pairwise distances in a cluster. Our algorithms work for arbitrary metric spaces as well as for points in d-dimensional space where the distance between two points x,y is measured by the square of the Euclidian distance (notice that this is not a metric). Our algorithms can be modified to handle other objective functions, such as minimizing the sum over all clusters of the total distance to the best choice for cluster center.