Embedding of rings in 2-D meshes and tori with faulty nodes

To increase the reliability of networks embedded in meshes or tori and to allow their use in the presence of faulty nodes, efficient fault-tolerant schemes in meshes and tori are necessary. In this paper, we present algorithms for embedding a ring in a mesh-type and torus-type multiprocessor networks in the event of node failures. In our approach, a mesh or torus is partitioned into 4 4 submeshes. Subgraphs (rings and linear arrays) are mapped in each submesh and thenmerged to form a large ring. Using this approach, we obtain the following results in a torus. Given any f 2 faulty nodes, a ring which is optimal can be found in a mesh. Also, given any f 4 faulty nodes, a ringwhich is optimal can be found in a torus. Furthermore, given f 4 faulty nodes, a Hamiltonian cycle can be found in a torus if and only if the number of even faulty nodes is equal to the number of odd faulty nodes. Even and odd refer to the sum of node’s coordinates