The capacitated K-center problem

The capacitated K-center problem is a basic facility location problem, wher e 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 fac ility to which it is assigned. Moreover, each facility may be assigned at m ost L vertices. This problem is known to be NP-hard. We give polynomial tim e approximation algorithms for two different versions of this problem that achieve approximation factors of 5 and 6. We also study some generalization s of this problem.