This paper presents and experimentally evaluates a new algorithm for efficient one-hop link-state routing in full-mesh networks. Prior techniques for this setting scale poorly, as each node incurs quadratic (n2) communication overhead to broadcast its link state to all other nodes. In contrast, in our algorithm each node exchanges routing state with only a small subset of overlay nodes determined by using a quorum system. Using a two round protocol, each node can find an optimal one-hop path to any other node using only n1.5 per-node communication. Our algorithm can also be used to find the optimal shortest path of arbitrary length using only n1.5 logn per-node communication. The algorithm is designed to be resilient to both node and link failures. We apply this algorithm to a Resilient Overlay Network (RON) system, and evaluate the results using a large-scale, globally distributed set of Internet hosts. The reduced communication overhead from using our improved full-mesh algorithm allows the creation of all-pairs routing overlays that scale to hundreds of nodes, without reducing the system's ability to rapidly find optimal routes.