Meshes with multiple buses

This paper considers mesh computers with buses, where each bus provides a broadcasting capability to the processors connected to it. We first disprove a published claim by showing that on a 2-dimensional mesh with a bus for each row, where each row must solve its own problem with data that is independent of all other rows, there are problems where the rows can cooperatively solve all subproblems faster than any single row can solve its own problem. As a corollary we obtain efficient solutions to some graph problems. We also consider the optimal layout of buses for a given dimension and number of buses per processor, where optimality is defined in terms of the time needed to simulate any other machine with the same constraints. Using new families of layouts, optimal or nearly optimal families of layouts are determined for each possible choice of dimension and number of buses per processor.