Virtual path network topology optimization using random graphs

Abstract

An algorithm is presented for designing the logical topology of the virtual path (VP) network, an important task in ATM network design. We prove that the algorithm provides a VP network topology that is asymptotically optimal with respect to both connectivity and the diameter of the network. These properties are combined with algorithmic simplicity and polynomial running time, thus overcoming the notorious optimality vs. dilemma. This result is made possible by applying the theory of random graphs to this type of networks. This theory has the methodological advantage of increased accuracy with growing network size, thus turning the curse of dimensionality into a blessing. Therefore, the paper exemplifies that the theory of random graphs, beyond supporting analysis purposes, may serve as a useful tool in the design of algorithms that overcome the scalability bottleneck, a problem that prevents current approaches from finding near-optimal solutions as today's networks grow in size and complexity.