Approximation algorithms for min-sum p-clustering Original Research Article

We consider the following problem: Given a graph with edge lengths satisfying the triangle inequality, partition its node set into p subsets, minimizing the total length of edges whose two ends are in the same subset. For this problem we present an approximation algorithm which comes to at most twice the optimal value. For clustering into two equal-sized sets, the exact bound on the maximum possible error ratio of our algorithm is between 1.686 and 1.7.