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We present Topology-based Geolocation (TBG), a novel approach to estimating the geographic location of arbitrary Internet hosts. We motivate our work by showing that 1) existing approaches, based on end-to-end delay measurements from a set of landmarks, fail to outperform much simpler techniques, and 2) the error of these approaches is strongly determined by the distance to the nearest landmark, even when triangulation is used to combine estimates from different landmarks. Our approach improves on these earlier techniques by leveraging network topology, along with measurements of network delay, to constrain host position. We convert topology and delay data into a set of constraints, then solve for router and host locations simultaneously. This approach improves the consistency of location estimates, reducing the error substantially for structured networks in our experiments on Abilene and Sprint. For networks with insufficient structural constraints, our techniques integrate external hints that are validated using measurements before being trusted. Together, these techniques lower the median estimation error for our university-based dataset to 67 km vs. 228 km for the best previous approach.