The discovery of links between resources within knowledge bases is of crucial importance to realize the vision of the Semantic Web. Addressing this task is especially challenging when dealing with geo-spatial datasets due to their sheer size and the potential complexity of single geo-spatial objects. Yet, so far, little attention has been paid to the characteristics of geo-spatial data within the context of link discovery. In this paper, we address this gap by presenting Orchid, a reduction-ratio-optimal link discovery approach designed especially for geo-spatial data. Orchid relies on a combination of the Hausdorff and orthodromic metrics to compute the distance between geo-spatial objects. We first present two novel approaches for the efficient computation of Hausdorff distances. Then, we present the space tiling approach implemented by Orchid and prove that it is optimal with respect to the reduction ratio that it can achieve. The evaluation of our approaches is carried out on three real datasets of different size and complexity. Our results suggest that our approaches to the computation of Hausdorff distances require two orders of magnitude less orthodromic distances computations to compare geographical data. Moreover, they require two orders of magnitude less time than a naive approach to achieve this goal. Finally, our results indicate that Orchid scales to large datasets while outperforming the state of the art significantly.