We introduce and study the donation center location problem, which has an additional application in network testing and may also be of independent interest as a general graph-theoretic problem. Given a set of agents and a set of centers, where agents have preferences over centers and centers have capacities, the goal is to open a subset of centers and to assign a maximum-sized subset of agents ...

The capacitated K-center problem is a fundamental facility location problem, where we are asked to locate K facilities in a graph, and to assign vertices to facilities, so as to minimize the maximum distance from a vertex to the facility to which it is assigned. Moreover, each facility may be assigned at most L vertices. This problem is known to be NP-hard. We give polynomial time approximation...

Given a set P of n points in R, a typical clustering problem asks for partitioning P into a family of k subsets {P1, . . . , Pk}, so that a certain objective function is minimized. The objective function depends on the application and varies. A typical clustering problem is the so-called centered clustering problem in which a representative point ci (or a q-flat) is chosen for each cluster Pi a...