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In this paper, we present a fast and practical algorithm for a map-matching problem searching a path on a given graph that minimizes Fréchet distance from a given trajectory, which is a natural measurement based on the sequential order of the trajectory. However, it sometimes costs seriously to compute the Fréchet distance while making correspondences to on a path on the graph in the order from the beginning of the trajectory as a naive method (as the definition) since it often occurs to backtrack and recompute. We developed an incremental technique for updating the Fréchet distance between the trajectory and a path to overcome the problem stated above. It enables the proposed algorithm to evaluate distances for any candidate paths faster than the naive one. In addition, we can adopt Dijkstra's graph searching manner due to the technique and omit to search and evaluate some useless candidates which have no relations with the solution. That also contributes to accelerate the algorithm. Experimental results show that our algorithm was more than fifty times faster than the algorithm of Alt (J. Algorithms 2003), which is formulated as a optimization problem repeating to solve decision problems with a binary search on a set of candidates of the Fréchet distance.

A Fast Algorithm for Matching Planar Maps with Minimum Fréchet Distances