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Consider a large wireless ad hoc network that facilitates communication between random pairs of network nodes. This paper investigates the size of routing tables as the number of nodes in the network increases. A routing protocol in a flat-label network is information-efficient if the amount of information at individual nodes required to route packets does not increase with the network size. It is shown that the shortest-path and straight-line routing algorithms are not information-efficient, i.e., these protocols can be implemented only when nodes' memory increases with the network size. On the other hand, it is established that there exists an information-efficient algorithm that routes packets correctly even if each node in the network is capable of storing information on a fixed number of destinations only.