Abstract
Abstract A basic problem in cluster analysis is how to partition the entities of a given set into a preassigned number of homogeneous subsets called clusters. The homogeneity of the clusters is often expressed as a function of a dissimilarity measure between entities. The objective function considered here is the minimization of the maximum dissimilarity between entities in the same cluster. It is shown that the clustering problem so defined is reducible to the problem of optimally coloring a sequence of graphs, and is NP-complete. An efficient algorithm is proposed and computational experience with problems involving up to 270 entities is reported on.
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