Schematization of road networks
Sergio Cabello, Mark de Berg, Steven van Dijk, Marc J. van Kreveld, Tycho Strijk · 2001
We study the problem of computing schematized versions of network maps , like railroad maps. Every path of the schematized map has two or three links with restricted orientations, and topologically, the schematized map must be equivalent to the input map. Our approach applies to several types of schematizations, and certain additional constraints can be added. In the general case our algorithm takes $O(n\log^3n)$ time, and when all paths in the input are monotone in some (not necessarily the same) direction, it runs in $O(n\log n)$ time.