Dynamic Programming for Minimal Cost Topology with Reliability Constraint

This paper addresses an NP-hard problem, called NTD-CR, to design a minimal-cost communication network topology that satisfies a pre-defined reliability constraint. Since reliability is always a major issue in the network design, the problem is practical for critical applications requiring minimized cost. The paper formulates a dynamic programming (DP) scheme to solve NTD-CR problem. DP approach, called DPCR-ST, generates the topology using a selected set of spanning trees of the network, STXmin. We propose three greedy heuristics to generate and order only k spanning trees of the network. Each heuristic allows DPCR-ST to enumerate STXmin using only k spanning trees, which improves the time complexity while producing near optimal topology. Simulations based on fully connected networks that contain up to 2.3×109 spanning trees show the merits of ordering methods and the effectiveness of our algorithm vis-a-vis four existing state-of-the-art techniques; DPCR-ST produces 81.5% optimal results, while using only 0.77% of the spanning trees contained in network.