Optimal Scheduling for UET/UET-UCT Generalized n-Dimensional Grid Task Graphs

Then-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. The two most frequently used scheduling models for grids are the unit execution time-zero communication delay (UET) and the unit execution time?unit communication time (UET-UCT). In this paper we introduce an enhanced model of then-dimensional grid by adding extra diagonal edges and allowing unequal boundaries for each dimension. For this generalized grid topology we establish the optimal makespan for both cases of UET/UET-UCT grids. Then we give a closed formula that calculates the minimum number of processors required to achieve the optimal makespan. Finally, we propose a low-complexity optimal time and processor scheduling strategy for both cases.

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