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Grid computing refers to the sharing of geographically distributed resources in order to accomplish a desired task. Grids are more secure and enable the job to be broken into chunks, each being executed in a parallel way. Computational Grids serve the purpose of processing a submitted job by finding the required resource from the grid. In implementing computational grids, resource discovery and task scheduling play a major role. Discovery of resources should be done at a minimum cost, avoiding the traversal to unnecessary nodes. Many approaches have been proposed in this area. In this paper, we propose the use of a three-layered, hierarchical, weighted tree structure with bitmaps representing the resources available at each node updated in a way to help the user to make a multi-attribute query. The higher level nodes are put together to form a structured Hyper Cube, resulting in a peer-to-peer fault tolerant and scalable system. Our proposed algorithm outperforms the other resource discovery mechanisms by drastically reducing the number of hops required and also avoiding traversal to unnecessary nodes in the tree. It is a more dynamic and fault tolerant resource discovery mechanism for peer-to-peer grids.