Optimal scheduling for UET-UCT generalized n-dimensional grid task graphs

The n-dimensional grid is one of the most representative patterns of data flow in parallel computation. The most frequently used scheduling models for grids is the unit execution-unit communication time (UET-UCT). We enhance the model of n-dimensional grid by adding extra diagonal edges. First, we calculate the optimal makespan for the generalized UET-UCT grid topology and then we establish the minimum number of processors required, to achieve the optimal makespan. Furthermore, we solve the scheduling problem for generalized n-dimensional grids by proposing an optimal time and space scheduling strategy. We thus prove that UET-UCT scheduling of generalized n-dimensional grids is low complexity tractable.