A Dynamic Programming Algorithm for Reliable Network Design

This paper addresses an NP-hard problem to design a network topology with maximum all-terminal reliability subject to a cost constraint, given the locations of the various computer centers (nodes), their connecting links, each link´s reliability and cost, and the maximum budget cost to install the links. Because cost is always a major focus in network design, this problem is practical for critical applications requiring maximized reliability. This paper first formulates a Dynamic Programming (DP) scheme to solve the problem. A DP approach, called DPA-1, generates the topology using all spanning trees of the network (ST_G). The paper shows that DPA-1 is optimal if the spanning trees are optimally ordered. Further, the paper describes an alternative DP algorithm, called DPA-2, that uses only k spanning trees ( k ≤ n, where n=|ST_G|) sorted in increasing weight and lexicographic order to improve the time efficiency of DPA-1 while producing similar results. Extensive simulations using hundreds of benchmark networks that contain up to 1.899¹⁰² spanning trees show the merits of using the sorting method, and the effectiveness of our algorithms. DPA-2 is able to generate 85% optimal results, while using only a small number of k spanning trees, and up to 16.83 CPU seconds. Furthermore, the non-optimal results are only up to 3.4% off from optimal for the simulated examples.