Solving problems on concurrent processors. Vol. 1: General techniques and regular problems
Solving problems on concurrent processors. Vol. 1: General techniques and regular problems
Emulation of Hypercube Architecture on Nearest-Neighbor Mesh-Connected Processing Elements
IEEE Transactions on Computers
Placement of the Processors of a Hypercube
IEEE Transactions on Computers
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Embeddings among meshes and tori
Journal of Parallel and Distributed Computing
Interconnection Networks for Multiprocessors and Multicomputers: Theory and Practice
Interconnection Networks for Multiprocessors and Multicomputers: Theory and Practice
SAC '98 Proceedings of the 1998 ACM symposium on Applied Computing
Hypercube Algorithms on Mesh Connected Multicomputers
IEEE Transactions on Parallel and Distributed Systems
Complete Exchange Algorithms for Meshes and Tori Using a Systematic Approach (Research Note)
Euro-Par '00 Proceedings from the 6th International Euro-Par Conference on Parallel Processing
Generalized parallel divide and conquer on 3D mesh and torus
Journal of Systems Architecture: the EUROMICRO Journal
The new torus network design based On 3-dimensional hypercube
ICACT'09 Proceedings of the 11th international conference on Advanced Communication Technology - Volume 1
A routing algorithm for multicast on hypercube multi-core architecture
Journal of Embedded Computing - Advanced Topics on Embedded Computing
Mapping semigroup array operations onto multicomputer with torus topology
Proceedings of the 5th International Conference on Ubiquitous Information Management and Communication
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Many parallel algorithms use hypercubes as the communication topology among their processes. When such algorithms are executed on hypercube multicomputers the communication cost is kept minimum since processes can be allocated to processors in such a way that only communication between neighbor processors is required. However, the scalability of hypercube multicomputers is constrained by the fact that the interconnection cost-per-node increases with the total number of nodes. From scalability point of view, meshes and toruses are more interesting classes of interconnection topologies. This paper focuses on the execution of algorithms with hypercube communication topology on multicomputers with mesh or torus interconnection topologies. The proposed approach is based on looking at different embeddings of hypercube graphs onto mesh or torus graphs. The paper concentrates on toruses since an already known embedding, which is called standard embedding, is optimal for meshes. In this paper, an embedding of hypercubes onto toruses of any given dimension is proposed. This novel embedding is called xor embedding. The paper presents a set of performance figures for both the standard and the xor embeddings and shows that the latter outperforms the former for any torus. In addition, it is proven that for a one-dimensional torus (a ring) the xor embedding is optimal in the sense that it minimizes the execution time of a class of parallel algorithms with hypercube topology. This class of algorithms is frequently found in real applications, such as FFT and some class of sorting algorithms.