A dynamic programming algorithm for the local access telecommunication network expansion problem

In this paper we consider the local access telecommunication network expansion problem, in which growing demand can be satis®ed by expanding cable capacities and/or installing concentrators in the network. The problem is known to be NP-hard. We prove that the problem is weakly NP-hard, and present a pseudo-polynomial dynamic programming algorithm for the problem, with time complexity O…nB2† and storage requirements O…nB†, where n refers to the size of the network, and B to an upper bound on concentrator capacity. The cost structure in the network is assumed to be decomposable, but may be non-convex, non-concave, and node and edge dependent otherwise. This allows for incorporation of many aspects occurring in practical planning problems. Computational results indicate that the algorithm is very ecient and can solve medium to large scale problems to optimality within (fractions of) seconds to minutes. Ó 2000 Elsevier Science B.V. All rights reserved.