A faster algorithm for matching planar maps under the weak Fréchet distance

We consider the problem of matching a polygonal curve of complexity p with an arbitrary curve on an embedded planar graph of complexity q. With the large amount of GPS and location trace data that have become available in recent years, algorithms for such problems have become increasingly important. Direct applications include matching a GPS trace to a given roadmap and indirect applications including building and querying databases of polygonal curves. As problem sizes increase, improvements in asymptotic runtime may prove to be useful and we present an algorithm which solves the problem with respect to the weak Fréchet distance in O(pq) time, which is an asymptotic improvement. In the process of doing so, we also provide a more intuitive and practical approach for the recursive division procedure used in Henzinger et al.’s shortest path algorithm for planar graphs. Unlike previous approaches to minimize the asymptotic complexity of calculating the Fréchet distance, our method does not involve parametric search, and hence is also more practical to implement. ∗Computer Science Department, Stanford University, Palo Alto CA 94305.