Scalable Ultrafast Almost-optimal Euclidean Shortest Paths

Abstract

We consider the problem of computing high-quality Euclidean shortest paths amidst obstacles on a large scale. By transferring and adapting speed-up techniques from the road network setting, we are able to compute source target paths for problem instances with several million obstacle vertices within few milliseconds after moderate preprocessing. We show experimentally that for small instances where optimal solutions are easily available on average our computed paths are less than 0.3% longer than the optimum. For large instances a new lower-bounding technique shows that on average our computed paths are less than 2% longer than the optimum paths. We compare our approach with the current state-of-the-art on problem instances derived from the OpenStreetMap project.