New Approximation Results for Resource Replication Problems

Barna Saha, Samir Khuller, Kanthi Sarpatwar. “New Approximation Results for Resource Replication Problems”Algorithmica

Abstract: In the Basic Resource Replication problem, we are given a graph,
embedded into a distance metric, and a set of data items. The goal is to assign one data item to each vertex so as to minimize the maximum distance any vertex has to travel to access all the data items. We consider several variants of this 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 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.