New approximation results for resource replication problems

Abstract

We consider several variants of a basic resource replication problem in this paper, and propose new approximation results for them. These problems are of fundamental interest in the areas of P2P networks, sensor networks and ad hoc networks, where optimal placement of replicas is the main bottleneck on performance. We observe that the threshold graph technique, which has been applied to several k-center type problems, yields simple and efficient approximation algorithms for resource replication problems. Our results range from positive (efficient, small constant factor, approximation algorithms) to extremely negative (impossibility of existence of any algorithm with non-trivial approximation guarantee, i.e., with positive approximation ratio) for different versions of the problem. © 2012 Springer-Verlag.