The load-distance balancing problem

Problems dealing with assignment of clients to servers have been widely studied. However, they usually do not model the fact that the delay incurred by a client is a function of both the distance to the assigned server and the load on this server, under a given assignment. We study a problem referred to as the Load-Distance Balancing problem (or LDB), where the objective is assigning a set of clients to a set of given servers. Each client suffers a delay that is the sum of the distance to its server and the congestion delay at this server, a non-decreasing function of the number of clients assigned to the server. We address two flavors of LDB – the first one seeking to minimize the maximum incurred delay, and the second one targeted for minimizing the average delay. For the first variation, we present hardness results, a best possible approximation algorithm, and an optimal algorithm for a special case of linear placement of clients and servers. For the second one, an optimal polynomial-time algorithm is presented.