Minimum sum of diameters clustering

Abstract

The problem of determining a partition of a given set of N entities into M clusters such that the sum of the diameters of these clusters is minimum has been studied by Brucker (1978). He proved that it is NP-complete for M≥3 and mentioned that its complexity was unknown for M=2. We provide an O(N3 log N) algorithm for this latter case. Moreover, we show that determining a partition into two clusters which minimizes any given function of the diameters can be done in O(N5) time. © 1987 Springer-Verlag.