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.