Distributed Aggregation/Disaggregation Algorithms for Optimal Routing in Data Networks

A new gradient projection algorithm using iterative aggregation and disaggregation is proposed and analyzed for box-constrained minimization problems. In a variation of the distributed computation model, the algorithm is shown to converge. As an important application, we also show how the algorithm is applied to optimal routing in a large interconnected data communication network. The aggregation/disaggregation method proposed results in a multi-level hierarchical clustering of a large network, which fits naturally the hierarchical topological structure of large networks. A numerical simulation of a 52-node network shows that the serial version of the algorithm, has 35% saving of the computational time as compared to a path-formulated gradient projection code developed by Bertsekas, Gendron and Tsai, which is among the fastest existing programs for path-formulated optimal routing.