Network Design: An Algorithm for the Access Facility Location Problem

In any network where a large number of widely dispersed "users" share a limited number of "resources," the strategy for access will play a large part in determining the cost and performance of the network. In this paper we consider a topological design aspect of the access problem. In particular, we consider the problem of locating "access facilities," or concentration points, to obtain an economic connection of users to resources. The problem is formulated as the locating of generic access facilities (GAF\´s) to obtain an economic connection of nodes (users) to a resource connection point (RESCOP). The nodes may be connected through multipoint lines, but with a constraint on the number of nodes which may share a single line. The GAF\´s are constrained in capacity, expressed as the number of nodes they can support, and have a cost associated with them. The basic solution technique presented is a heuristic algorithm characterized by the following four steps. 1) Simplify the problem to a point-to-point problem by replacing clusters of nodes by single "center-of-mass" (COM) nodes. 2) Partition the reduced set of COM nodes by applying an Add algorithm, resulting in one of the COM nodes selected as a GAF site. 3) Select one of the original nodes as a real GAF site in each partition by examining the original nodes closest to the COM node selected in the Add algorithm, and selecting the best. 4) Apply a line-layout algorithm to each partition, with its selected GAF site serving as the central node.