Reconfiguration of two-dimensional meshes embedded in hypercubes

Proposes a method of reconfiguring 2D meshes embedded in hypercubes. Our reconfiguration for link failures consists of two stages. The first stage assigns the d dimensions of the hypercubes to two directions with respect to rows and columns in the mesh, so that the number of disconnected pairs with adjacent rows and columns becomes smaller. The second stage re-establishes the mesh communication by assigning the Cartesian product of two Gray code sequences, which represent the order of healthy rows and columns to every node. We introduce graphs with edges corresponding to connections between rows or columns, and search the sequences. Then either an approach based on the depth-first search or one based on a genetic algorithm is applied to the graphs. The approach is made valid for node failures by regarding a faulty node as a node without healthy links. Simulation results show that our method reconfigures embedded meshes efficiently with relatively short computation time.