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We analyze the asymptotic cost of discovering a route within a flat ad hoc network and we show that one can discover a route with cost that is proportional only to the area of the network and that is independent of the number of network nodes. Furthermore, we show that this is optimal and that bordercasting (a query propagation protocol where a node retransmits a query to a set of nodes at some hop-distance away) possesses this density-independence property. We present the design of bordercastdoi:10.1007/s10776-006-0055-9 fatcat:xfd5lqmqxza35mdktwow6cbprm