Broadcasting and routing in faulty mesh networks

Broadcasting is a data communication task in which one processor sends the same message to all other processors. Routing is a task where a source processor sends a message to a destination processor. A faulty node is in an error state and cannot participate in the activities or the communication in a given network. In this paper, we consider the family of mesh networks, which include the mesh connected computer (MCC), k-dimensional mesh, torus, and k-ary n-cube. Our goal is to design routing and broadcasting algorithms which will use local knowledge of faults, no additional resources, will work for an arbitrary number and structure of faults, will guarantee delivery to all nodes connected to the source, and will remain optimal in a fault free mesh. We did not find any solution in literature to satisfy these desirable properties. Our routing and broadcasting schemes for MCCs and tori, and our broadcasting algorithm for the all-port model on any faulty mesh network satisfy all of these properties. For routing and broadcasting in a one-port model in higher dimensions, a condition on fault structure needs to be met. We propose a new broadcasting algorithm which guarantees delivery to all processors connected to the source in the all-port model of faulty meshes. We then describe a routing algorithm that guarantees delivery in faulty MCCs and tori, the connectivity of the source and destination being the only obvious requirement. The algorithm can be extended to faulty k-D meshes and k-ary n-cubes, where the delivery will be guaranteed if healthy nodes in every 2-D submesh (sub-tori) remain connected. We then describe broadcasting algorithms for the one-port model, which again guarantee delivery to all connected processors in two-dimensional cases, and guarantee delivery in k-dimensional cases if healthy processors in every 2-D submesh (sub-tori) remain connected

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