Dynamic programming for minimal cost topology with two terminal reliability constraint

This paper addresses an NP-complete problem, called NTD-CR, to design a minimal-cost communication network topology that satisfies a pre-defined two terminal reliability constraint, given the locations of the various computer centers (nodes), their connecting links, each link´s reliability and cost, and the required reliability for the network to operate. This paper formulates a dynamic programming (DP) scheme to solve the NTD-CR problem. DP approach, called DPCR-P, generates the topology using a selected set of paths of the network. We propose two different greedy heuristics to generate and order only k≤n paths, where n is the total number of paths in the network. Each heuristic allows DPCR-P to enumerate the selected paths using only k paths, which improves the time complexity while producing near optimal topology. Extensive simulations using benchmark networks with various sizes show the merits of path-orders, and the effectiveness of our approach. DPCR-P is able to generate 91% optimal results on the networks using only 8.89% to 27.5% of all paths in the networks. Further, its non-optimal results are no more than 10.97% off from optimal.