Grid Resource Discovery Service is a fundamental problem that has been the focus of research in the recent past. We propose a scheme that presents essential characteristics for efficient, self-configuring and fault-tolerant resource discovery able to handle dynamic attributes such as memory capacity. Our approach consists of an overlay network with a hypercube topology connecting the grid nodes and a scalable, fault-tolerant, self-configuring search algorithm. By design, the algorithm improves the probability of reaching all working nodes in the system, even in the presence of non-alive nodes (inaccessible, crashed or nodes loaded by heavy traffic). We analyze the static resilience of the approach presented, which is the measure of how well the algorithm can discover resources without having to update the routing tables. The results show that the presented approach has significantly high static resilience.