Computational Complexity of the Problem of Choosing Typical Representatives in a 2-Clustering of a Finite Set of Points in a Metric Space

We consider the computational complexity of one extremal problem of choosing a subsetof p points from some given 2-clustering of a finite set in a metric space. Thechosen subset of points has to describe the given clusters in the best way from the viewpoint ofsome geometric criterion. This is a formalization of an applied problem of data mining whichconsists in finding a subset of typical representatives of a dataset composed of two classes basedon the function of rival similarity. The problem is proved to be NP-hard. To this end, wepolynomially reduce to the problem one of the well-known problems NP-hard in the strong sense,the p-median problem.