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In this paper we focus on the map matching problem where the goal is to finda path through a planar graph such that the path through the vertices closelymatches a given polygonal curve. The map matching problem is usually approachedwith the Fr\'echet distance matching the edges of the path as well. Here, weformally define the discrete map matching problem based on the discreteFr\'echet distance. We then look at the complexities of some variations of theproblem which allow for vertices in the graph to be unique or reused, andwhether there is a bound on the length of the path or the number of verticesfrom the graph used in the path. We prove several of these problems to beNP-complete, and then conclude the paper with some open questions.

Intermittent Map Matching with the Discrete Fr\'echet Distance