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Accurate and timely identification of the router-level topology of the Internet is one of the major unresolved problems in Internet research. Topology recovery via tomographic inference is potentially an attractive complement to standard methods that use TTL-limited probes. In this paper, we describe new techniques that aim toward the practical use of tomographic inference for accurate router-level topology measurement. Specifically, prior tomographic techniques have required an infeasible number of probes for accurate, large scale topology recovery. We introduce a Depth-First Search (DFS) Ordering algorithm that clusters end host probe targets based on shared infrastructure, and enables the logical tree topology of the network to be recovered accurately and efficiently. We evaluate the capabilities of our DFS Ordering topology recovery algorithm in simulation and find that our method uses 94% fewer probes than exhaustive methods and 50% fewer than the current state-of-the-art. We also present results from a case study in the live Internet where we show that DFS Ordering can recover the logical router-level topology more accurately and with fewer probes than prior techniques.