The Distributed p-Median Problem in Computer Networks

Abstract

Many distributed services in computer networks rely on a set of active facilities that are selected among a potentially large number of candidates. The active facilities then contribute and cooperate to deliver a specific service to the users of the distributed system. In this scenario graph partitioning or clustering is often adopted to determine the most efficient locations of the facilities. The identification of the optimal set of facility locations is known as the p-median problem in networks, is NP-hard and is typically solved by using heuristic methods. The goal is to select p locations among all candidate network nodes such that some cost function is minimised. A typical example of such a function is the overall communication cost to deliver the service to the users of the distributed system. Locating facilities in near-optimal locations has been extensively studied for different application domains. Most of these studies have investigated sequential algorithms and centralised approaches. However, centralised approaches are practically infeasible in large-scale and dynamic networks, where the problem is inherently distributed or because of the large communication overhead and memory requirements for gathering complete information about the network topology and the users. In this work distributed approaches to the p-median problem are investigated. Two solutions are proposed for addressing the facility locations problem in a fully distributed environment. Two different iterative heuristic approaches are applied to gradually improve a random initial solution and to converge to a final solution with a local minimum of the overall cost. While the first approach adopts a fine granularity by identifying a single change to improve the solution at each iteration, the second approach applies changes to every component of the solution at each iteration. An experimental comparative analysis based on simulations has shown that the approach with a finer granularity is able to deliver a better optimisation of the overall cost with longer convergence time. Both approaches have excellent scalability and provide an effective tool to optimise the facility locations from within the network. No prior knowledge of the system is required, no data needs to be gathered in a centralised server and the same process is used to identify and to deploy the facility locations solution in the network since the process is fully decentralised.