Practical topologically safe rounding of geographic networks

Abstract

We consider the problem of accurately representing geographic networks at reduced coordinate precision. We require that vertices are placed on a grid and the network topology is retained, that is, we are not allowed to introduce intersections or collapse faces. Minimizing the "rounding error" in this setting is known to be NP-hard and no practical methods, even heuristic, are known. We demonstrate a two-stage simulated annealing algorithm that focuses on finding a feasible solution first, then switches to optimizing the rounding error; a straightforward annealing approach without stage one has difficulty finding any feasible solution at all. We discuss various feasibility procedures and evaluate their applicability on geographic networks. Datasets and an implementation in C++ are available at: https://github.com/tcvdijk/armstrong.