Approximation Algorithms for Dispersion Problems

Dispersion problems involve arranging a set of points as far away from each other as possible. They have numerous applications in the location of facilities and in management decision science. We suggest a simple formalism that lets us describe different dispersal problems in a uniform way. We present several algorithms and hardness results for dispersion problems using different natural measures of remoteness, some of which have been studied previously in the literature and others that we introduce; in particular, we give the first algorithm with a nontrivial performance guarantee for the problem of locating a set of points such that the sum of their distances to their nearest neighbor in the set is maximized.