Routing algorithms with time and message complexities that are provably low and independent of the total number of nodes in the network are essential for the design and operation of very large scale wireless mobile ad hoc networks (MANETs). In this paper, we develop and analyze Cluster Overlay Broadcast (COB), a low-complexity routing algorithm for MANETs. COB runs on top of a one-hop cluster cover of the network, which can be created and maintained using, for instance, the Least Cluster Change (LCC) algorithm. We formally prove that the LCC algorithm maintains a cluster cover with a constant density of cluster leaders with minimal update cost. COB discovers routes by flooding (broadcasting) route requests through the network of cluster leaders with a doubling radius technique. Building on the constant density property of the network of cluster leaders, we formally prove that, if there exists a route from a source to a destination node with a minimum hop count of A, then COB discovers a route with at most O(/spl Delta/) hops from the source to the destination node in at most O(/spl Delta/) time and by sending at Most O(/spl Delta//sup 2/) messages. We prove this result for arbitrary node distributions and mobility patterns and also show that COB adapts asymptotically optimally to the mobility of the nodes. In our simulation experiments, we examine the network layer performance of COB, compare it with Dynamic Source Routing, and investigate the impact of the MAC layer on COB routing.