Optimal scheduling for UET-UCT grids into fixed number of processors

The n-dimensional grid is one of the most representative patterns of data flow in parallel computation. Many scientific algorithms, which require nearest neighbor communication in a lattice space, are modeled by a task graph with the properties of a simple or enhanced grid. In this paper we consider an enhanced model of the n-dimensional grid by adding extra diagonal edges and allowing unequal boundaries for each dimension. First, we calculate the optimal makespan for the generalized UET-UCT (Unit Execution Time-Unit Communication Time) grid topology and then, we establish the minimum number of processors required, to achieve the optimal makespan. We present the optimal time schedule, using unbounded and bounded number of processors, without allowing task duplication. This paper proves that UET-UCT scheduling of generalized n-dimensional grids into fixed number of processors is low complexity tractable.