The layout of virtual paths in ATM networks

We study the problem of designing a layout of virtual paths (VPs) on a given ATM network. We first define a mathematical model that captures the characteristics of virtual paths. In this model, we define the general VP layout problem, and a more restricted case; while the general case layout should cater connections between any pair of nodes in the network, the restricted case layout should only cater connections between a specific node to the other nodes. For the latter case, we present an algorithm that finds a layout by decomposing the network into subnetworks and operating on each subnetwork, recursively; we prove an upper bound on the optimality of the resulting layout and a matching lower bound for the problem, that are tight under certain realistic assumptions. Finally, we show how the solution for the restricted case is used as a building block in various solutions to more general cases (trees, meshes, K-separable networks, and general topology networks) and prove a lower bound for some of our results. The results exhibit a tradeoff between the efficiency of the call setup and both the utilization of the VP routing tables and the overhead during recovery from link disconnections.