Modeling and Practical Evaluation of a Service Location Problem in Large Scale Networks

Abstract

We consider a generalization of a classical optimization problem related to server and replica location problems in networks. More precisely, we suppose that a set of users distributed over a network wish to have access to a particular service proposed by a set of providers. The aim is then to distinguish a set of service providers able to offer a sufficient amount of resources in order to satisfy the requests of the clients. Moreover, a quality of service following some requirements in terms of latencies is desirable. A smart repartition of the servers in the network may also ensure good fault tolerance properties. We model this problem as a variant of Bin Packing, namely Bin Packing under Distance Constraint(BPDC) where the goal is to build a minimal number of bins(i.e. to choose a minimal number of servers) so that (i) each client is associated to exactly one server, (ii) the capacity of the server is large enough to satisfy the requests of its clients and (iii) the distance between two clients associated to the same server is minimized. We prove that this problem is hard to approximate even when using resource augmentation techniques : we compare the number of obtained bins when using polynomial time algorithms allowed to build bins of diameter at most beta.dmax, for beta > 1, to the optimal number of bins of diameter at most dmax. On the one hand, we prove that (i) if _ = (2âˆ'epsilon), BPDC is hard to approximate within any constant approximation ratio, for any epsilon > 0, and that (ii) BPDC is hard to approximate at a ratio lower than 3/2 even if resource augmentation is used. On the other hand, if beta = 2, we propose a polynomial time approximation algorithm for BPDC with approximation ratio 7/3 in the general case. We show how to turn an approximation algorithm for BPDC into an approximation algorithm for the non-uniform capacitated K-center problem and vice-versa. Then, we present a comparison of the quality of results for BPDC in the context of several Internet latency embedding tools such as Sequoia and Vivaldi, using datasets based on Planet Lab latency measurements.