Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
IEEE Transactions on Parallel and Distributed Systems
Resource Placement in Torus-Based Networks
IEEE Transactions on Computers
Lee Distance and Topological Properties of k-ary n-cubes
IEEE Transactions on Computers
On Optimal Placements of Processors in Tori Networks
SPDP '96 Proceedings of the 8th IEEE Symposium on Parallel and Distributed Processing (SPDP '96)
Lower Bounds on Communication Loads and Optimal Placements in Torus Networks
IEEE Transactions on Computers
| Hi-index | 0.00 |
Fully-populated tori, where every node has a processor attached, do not scale well since load on edges increases superlinearly with network size under heavy communication, resulting in a degradation in network throughput. In a partially-populated network, processors are placed on a subset of available nodes, and a routing algorithm is specified among the processors.Analogous to multistage networks, it is desirable to have the total number of messages being routed through a particular edge increase at most linearly with the size of the placement on torus networks. Recently, Blaum, Bruck, Pifarr茅 and Sanz investigated placements and provided both a lower bound, and optimal placements in the cases of 2 and 3-dimensional k-tori, consisting of k and k2 processors, respectively.In this paper we show formally that to achieve linear load in a d-dimensional k-torus, the number of processors in the placement must be O(kd-1). We use this to construct a tighter lower bound for the maximum load of a placement for 4 or more dimensions. Based on these results, we give optimal placements and their corresponding routing algorithms in tori with arbitrary number of dimensions.