Approximate Map Matching with respect to the Fréchet Distance

We extend recent results using curve simplification for approximating the Fréchet distance of realistic curves in near linear time to map matching: the problem of matching a curve in an embedded graph. We show that the theoretical bounds on the running time of the previous result still hold if only one of the curves is simplified during the course of the approximation algorithm. This enables our extension to the case of map matching under the assumption that the graph is φ-low density for a constant φ. We present experimental evidence for this assumption and implement the extended approximate matching algorithm. We show that it performs well on real world data, such as GPS traces and road networks of urban areas. In particular, it is able to perform matching tasks that took several hours with the exact matching algorithm in under a second.