Decremental Clustering for the Solution of p -Dispersion Problems to Proven Optimality

Abstract

Given n points, a symmetric dissimilarity matrix D of dimensions n × n, and an integer p ? 2, the p-dispersion problem (pDP) consists of selecting a subset of exactly p points in such a way that the minimum dissimilarity between any pair of selected points is maximum. The pDP is [Formula: see text] when p is an input of the problem. We propose a decremental clustering method to reduce the problem to the solution of a series of smaller pDPs until reaching proven optimality. A k-means algorithm is used to construct and refine the clusterings along the algorithm’s execution. The proposed method can handle problems orders of magnitude larger than the limits of the state-of-the-art solver for the pDP for small values of p.