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Geometric routing has been proposed in literature as a memory-efficient alternative to traditional lookup-based routing and forwarding algorithms. However, existing geometric routing schemes lack the ability to address network link and node failures in a natural way, while maintaining a low path stretch. The main contribution of this paper is a novel routing scheme called Greedy Forest Routing (GFR) based on the principles of geometric routing. By employing a graph embedding based on low-redundancy spanning trees, its fault-tolerant characteristics are enhanced. Using a multi-dimensional tree embedding enables natural traffic redirection while still attaining a low average hop count.