Estimating the distribution of travel times on a transportation network from vehicle GPS data requires finding the closest path on the network to a trajectory of GPS points. In this work, we develop: 1) an efficient algorithm (MOE) to find such a path and able to detect the presence of cycles; 2) a faster but less accurate heuristic (MMH) unable to detect cycles. We present computational results that compare these algorithms, for different sampling rates and GPS sensitivities, using GPS trajectories of three networks: A grid graph and street networks of Santiago and Seattle. We show that MOE (MMH) returns in seconds (hundredths of second) paths where on average 93% (91%) of the edges are within a corridor of one metre from the real path.