UET scheduling with unit interprocessor communication delays
Discrete Applied Mathematics
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Towards an architecture-independent analysis of parallel algorithms
SIAM Journal on Computing
Optimal scheduling for UET/VET-UCT generalized n-dimensional grid task graphs
Journal of Parallel and Distributed Computing
On the Granularity and Clustering of Directed Acyclic Task Graphs
IEEE Transactions on Parallel and Distributed Systems
DSC: Scheduling Parallel Tasks on an Unbounded Number of Processors
IEEE Transactions on Parallel and Distributed Systems
Automatic Hardware Synthesis of Nested Loops Using UET Grids and VHDL
HPCN Europe '97 Proceedings of the International Conference and Exhibition on High-Performance Computing and Networking
Optimal Scheduling for UET-UCT Generalized n-Dimensional Grid Task Graphs
IPPS '97 Proceedings of the 11th International Symposium on Parallel Processing
Optimal Schedules for d-D Grid Graphs with Communication Delays (Extended Abstract)
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
NP-complete scheduling problems
Journal of Computer and System Sciences
Scheduling UET grids with unit communication time delays into unbounded/fixed number of processors
Highly parallel computaions
Guarantee the victorious probability of grid resources in the competition for finite tasks
GPC'08 Proceedings of the 3rd international conference on Advances in grid and pervasive computing
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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.