Applying k-means Method to the Modified Bottleneck Assignment Problem in Vector Case

Abstract

In this study, we deal with the vector case's bottleneck assignment problem. Each edge's cost is introduced by the sum of the vertices which are assigned. This problem is NP-complete. We show an idea that we use a clustering method to divide the problem to partial ones. Each vertices' set is divided into subsets by a non-hierarchical clustering method. We make the optimal combination of the subsets, then vertices in the subset are corresponded according to the subsets' combinations. We examine our proposed algorithm in effectiveness by numerical experiments.