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Inference of the routing topology and link performance from a node to a set of other nodes is an important component of network monitoring and application design. In this paper we propose a general framework for designing topology inference algorithms based on additive metrics. Our framework allows the integration of both end-to-end packet probing measurements and traceroute type measurements. Based on this framework we design several computationally efficient topology inference algorithms. In particular, we propose a novel sequential topology inference algorithm to address the probing scalability problem and handle dynamic node joining and leaving. We provide sufficient conditions for the correctness of our algorithms and derive lower bounds on the probability of correct topology inference. We conduct Internet experiments to evaluate and demonstrate the effectiveness of our algorithms.