Abstract not found

We present a natural greedy algorithm for the metric uncapacitated facility location problem and use the method of dual fitting to analyze its approximation ratio, which turns out to be 1.861. The running time of our algorithm is O(m log m), where m is the total number of edges in the underlying complete bipartite graph between cities and facilities. We use our algorithm to improve recent results for some variants of the problem, such as the fault tolerant and outlier versions. In addition, we introduce a new variant which can be seen as a special case of the concave cost version of this problem.

Abstract not found

In the k-level uncapacitated facility location problem, we have a set of demand points where clients are located. The demand of each client is known. Facilities have to be located at given sites in orde to service the clients, and each client is to be serviced by a sequence of k different facilities, each of which belongs to a distinct level. Thee are no capacity restrictions on the facilities. There is a positive fixed cost of setting up a facility, and a pe unit cost of shipping goods between each pair of locations. We assume that these distances are all nonnegative and satisfy the triangle inequality. The problem is to find an assignment of each client to a sequence of k facilities, one at each level, so that the demand of each client is satisfied, for which the sum of the setup costs and the service costs is minimized.

The cost structures for resource allocation in many network design problems obey economies of scale, meaning that the cost per unit resource becomes cheaper as the amount of resources allocated increases. For instance, if we are purchasing cables to route data in a network, the cost per unit bandwidth reduces as the bandwidth we need to route increases. Another feature of resource allocation is granularity, meaning that the resource can only be purchased in multiples of a certain minimum quantity. Again, in the context of purchasing cables in a network, the minimum capacity cable available might be a T1 line with capacity 1 Mbps. In this