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A Methodology for Design and Applications of Parallel Computers

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dc.contributor.advisor Deng, Yuefan en_US
dc.contributor.author Zhang, Peng en_US
dc.contributor.other Department of Applied Mathematics and Statistics en_US
dc.date.accessioned 2013-05-24T16:38:22Z
dc.date.accessioned 2015-04-24T14:45:06Z
dc.date.available 2013-05-24T16:38:22Z
dc.date.available 2015-04-24T14:45:06Z
dc.date.issued 2011-12-01 en_US
dc.identifier.uri http://hdl.handle.net/1951/60291 en_US
dc.identifier.uri http://hdl.handle.net/11401/70917 en_US
dc.description 95 pg. en_US
dc.description.abstract This dissertation focuses on two aspects of parallel computing, i.e., development and applications of parallel computers. First, we introduce a new technique by strategically interlacing bypass rings to torus (iBT network) for generating more efficient grid-like interconnection networks. Second, we derive an algebraic formulation of mapping tasks to parallel computers with complex network architectures for realizing their potentials. Compared to the widely adopted mesh and torus network topologies, our new iBT network has many superior characteristics: (1) its network diameter and average node-to-node distances are significantly reduced; (2) the simplicity of a grid-like layout is preserved; (3) it outperforms other bypass torus networks; and (4) it has far more flexible network sizes. A mathematical model is further devised to analyze the dependencies of the iBT network diameters on bypass schemes, thus enabling discovery of a class of the most efficient bypass schemes for a given node degree and network size. Additionally, a pipelined broadcast algorithm for the all-port nodal ability is present and analyzed, demonstrating the collective performance. The iBT networks is finding broad applications in designing higher-dimensional and larger-scale parallel computers as the 3-D torus networks have done for parallel computers with fewer processors. We have developed a new formulation for the task mapping in efficient application of a parallel computer with complex networks such as iBT. The fact that the supply matrix, characterizing the network topologies, exhibits enormous symmetries allows us the transformation of the demand matrix measuring the communication demands of applications to derive a hop-byte objective function in terms of the eigen properties. This new eigen-based formulation dramatically reduces the complexity of finding the solutions for the objective functions from the conventional and widely adopted graph theory-based formulations. Numerical experiments with simulated annealing demonstrate such gains. This formulation enables solution of critical task mapping problems on large-scale parallel computers. en_US
dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Applied mathematics en_US
dc.subject.other interconnection network, interlaced bypass torus, optimization, parallel computer, parallel computing, task mapping en_US
dc.title A Methodology for Design and Applications of Parallel Computers en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Lindquist, William Brent en_US
dc.contributor.committeemember Mitchell, Joseph S.B.McGuigan, Michael en_US
dc.contributor.committeemember Chen, Dong en_US

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