To avoid exponential proliferation of explorer packets through a LAN/Bridge network, each bridge gathers information sufficient to compute routes through the network by sharing routing messages with other bridges. Then, to find a route from a particular source end system to a particular destination end system, a broadcast message identifying the desired source and destination is sent to the bridges. In response, the bridges compute the optimal route to each attached LAN, convert the broadcast message into one or more counterfeit explorer messages by incorporating these routes, and then transmit the counterfeit explorer messages to the LANs for which the incorporated route was computed. The destination end system then receives one or more of the counterfeit explorer messages and responds to the source end system as if the counterfeit explorer message was genuine.