Convergence Analysis and Quality Criteria for an Iterative Schematization of Networks

Schematic networks are linear abstractions of functional networks, such as route networks. Lines in the original network are modified in order to produce a schematic network which satisfies a set of constraints chosen to design the network. A method is described which accomplishes this line transformation using an iterative improvement technique driven by design constraints. The method maintains topological characteristics of the network by the use of simple geometric operations and tests. The iterative process can be repeated until the line displacements become small enough or until it meets user defined stopping criteria. Experimental results are provided to examine the acceptability of outcomes and the convergence of the applied iterative technique. Criteria for measuring the quality of results, as well as for stopping the iterative approach are presented.