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Networks based on Ethernet bridging scale poorly as bridges flood the entire network repeatedly, and several schemes have been proposed to mitigate this flooding problem, however, none have managed to eliminate flooding completely. We present Automatic Integrated Routing (AIR) as the first routing protocol that eliminates flooding by assigning prefix labels to switches and building a Distributed Hash Table (DHT). The DHT maps host identifiers to the prefix labels of the switches through which they connect to the network. Each switch is assigned a prefix label using neighbor-to-neighbor messages. Prefix labels denote the locations of the switches in the network, and the prefix labels of any two switches automatically determine one or multiple routes between them. The DHT stores the mapping between the name of a host and its network location (prefix label) in a scalable fashion, with any one switch storing only a fraction of all the mappings. In contrast, prior approaches using DHTs to resolve host names incur the communication and storage overhead introduced by an underlying link-state routing protocol. Results using packet-level traces of Internet traffic demonstrate that AIR attains performance gains of orders of magnitude over Ethernet bridging and prior DHT-based schemes.