K-center problems

Abstract

We consider a generalization of the classical K-center problem with capacities, demands, and outliers. The capacitated K-center problem adds a constraint to the original K-center problem of every vertex having a capacity assigned to it. This means that if a vertex is selected as a center, then it can serve as a center to at most its capacity. The K-center with demand version where each vertex i is required to have a set of αi (αi <= k) centers close to it. We define the Non-uniform Demand version where values of αi vary for each vertex. We try to solve the capacitated K-center with non-uniform demand problem which is a generalization of the capacitated and the non-uniform demand versions of the K-center problems stated above. We also try to understand and solve another generalization of allowing outliers in the K-center problem