Global Navigation Satellite Systems (GNSS) such as Global Positioning Systems (GPS) are employed in different Intelligent Transportation Systems (ITS) applications to determine vehicle routes. However, the map-matching problem emerges when GPS measurements are assigned to incorrect road segments on a digital map due to the complexities of the road network and errors from different sources when capturing GPS data. This study presents a Topological Map-Matching Algorithm (TMMA) for determining correct waste collection vehicle routes using GPS measurements in an offline context to help improve solid waste collection services and compute proper performance measures. The TMMA is applied to a real-world case study with ten waste collection routes in the commune of Renca in Santiago, Chile. Overall, results indicate that the accuracy of the algorithm is greater than 90%, and small percentages of false negative cases with unsnapped GPS data points are obtained for most vehicle routes. The sensitivity analysis suggests that larger buffer sizes and higher speed tolerances yield the best solution quality and execution times.