Computing minimum length paths of a given homotopy class

AbstractIn this paper, we show that the universal covering space of a surface can be used to unify previous results on computing paths in a simple polygon. We optimize a given path among obstacles in the plane under the Euclidean and link metrics and under polygonal convex distance functions. Besides revealing connections between the minimum paths under these three distance functions, the framework provided by the universal cover leads to simplified linear-time algorithms for shortest path trees, for minimum-link paths in simple polygons, and for paths restricted to c given orientations