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AN ARRAY ASSIGNMENT METHOD FOR parallel computing systemS

International Journal of High Speed computing 1994年第1期6卷 81-100页

作者： JIANZHONG LI JAIDEEP SRIVASTAVA Computer Science Department P.O. Box 261 Heilongjiang University Harbin 150080 P.R. China Computer Science Department 4–192 EECS Building 200 Union Street S.E. University of Minnesota Minneapolis MN 55455 USA

In parallel computing systems, a crucial factor that can limit parallelism is the distribution of operands, which usually are vectors, matrices or higher dimensional arrays, among parallel memory modules. In this paper, we introduce a method of assignment of high dimensional arrays, which include vectors and matrices as special cases, to parallel memory modules of parallel computing systems. Our analysis shows that the method achieves maximum parallelism for a very high percentage of array operations. We have derived the exact conditions under which optimality is achieved. Also provided are the worst and average case bounds on array operation performance.

关键词： parallel computing system parallel memory modules high dimensional array high dimensional array assignment

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Optimal Path Embedding in the Exchanged Crossed Cube

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Journal of Computer Science & Technology 2017年第3期32卷 618-629页

作者： Dong-Fang Zhou Jian-Xi Fan Cheng-Kuan Lin Bao-Lei Cheng Jing-Ya Zhou Zhao Liu School of Computer Science and Technology Soochow University Suzhou 215006 China Collaborative Innovation Center of Novel Software Technology and Industrialization Nanjing University Nanjing 210000 China

The （s＋t＋1）-dimensional exchanged crossed cube, denoted as ECQ（s, t）, combines the strong points of the exchanged hypercube and the crossed cube. It has been proven that ECQ（s, t） has more attractive properties than other variations of the fundamental hypercube in terms of fewer edges, lower cost factor and smaller diameter. In this paper, we study the embedding of paths of distinct lengths between any two different vertices in ECQ（s, t）. We prove the result in ECQ（s, t）： if s≥3, t≥3, for any two different vertices, all paths whose lengths are between max{9,「s＋1/2」＋「t＋1/2＋4}and 2s＋t＋1？1 can be embedded between the two vertices with dilation 1. Note that the diameter of ECQ（s, t） is「s＋1/2 」＋「t＋1/2 」＋2. The obtained result is optimal in the sense that the dilations of path embeddings are all 1. The result reveals the fact that ECQ（s, t） preserves the path embedding capability to a large extent, while it only has about one half edges of CQn.

关键词： interconnection network exchanged crossed cube path embedding parallel computing system

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Embedding meshes into locally twisted cubes

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INFORMATION SCIENCES 2010年第19期180卷 3794-3805页

作者： Han, Yuejuan Fan, Jianxi Zhang, Shukui Yang, Jiwen Qian, Peide Soochow Univ Sch Comp Sci & Technol Suzhou Peoples R China Soochow Univ Network Ctr Suzhou 215006 Peoples R China

As a newly introduced interconnection network for parallel computing, the locally twisted cube possesses many desirable properties. In this paper, mesh embeddings in locally twisted cubes are studied. Let LTQ(n)(V,E) denote the n-dimensional locally twisted cube. We present three major results in this paper: (1) For any integer n >= 1, a 2 x 2(n-1) mesh can be embedded in LTQ(n) with dilation 1 and expansion 1. (2) For any integer n >= 4, two node-disjoint 4 x 2(n-3) meshes can be embedded in LTQ(n) with dilation 1 and expansion 2. (3) For any integer n >= 3, a 4 x (2(n-2) - 1) mesh can be embedded in LTQ(n) with dilation 2. The first two results are optimal in the sense that the dilations of all embeddings are 1. The embedding of the 2 x 2(n-1) mesh is also optimal in terms of expansion. We also present the analysis of 2p x 2q mesh embedding in locally twisted cubes. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Locally twisted cube Mesh Embedding Dilation Expansion parallel computing system

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Optimal fault-tolerant embedding of paths in twisted cubes

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JOURNAL OF parallel AND DISTRIBUTED computing 2007年第2期67卷 205-214页

作者： Fan, Jianxi Lin, Xiaola Pan, Yi Jia, Xiaohua City Univ Hong Kong Dept Comp Sci Hong Kong Hong Kong Peoples R China Sun Yat Sen Univ Coll Informat Sci & Technol Guangzhou Peoples R China Georgia State Univ Dept Comp Sci Atlanta GA 30303 USA

The twisted cube is an important variation of the hypercube. It possesses many desirable properties for interconnection networks. In this paper, we study fault-tolerant embedding of paths in twisted cubes. Let TQ(n)(V, E) denote the n-dimensional twisted cube. We prove that a path of length I can be embedded between any two distinct nodes with dilation 1 for any faulty set F subset of V(T Q(n)) boolean OR E(T Q(n)) with \F\ <= n - 3 and any integer l with 2(n-1) - 1 <= l <= \V (T Q(n) - F)\-1 (n >= 3). This result is optimal in the sense that the embedding has the smallest dilation 1. The result is also complete in the sense that the two bounds on path length l and faulty set size \F\ for a successful embedding are tight. That is, the result does not hold if l <= 2(n-1) - 2 or \F\ >= n - 2. We also extend the result on (n - 3) -Hamiltonian connectivity of T Q(n) in the literature. (C) 2006 Elsevier Inc. All rights reserved.

关键词： twisted cube fault tolerant path embedding dilation parallel computing system

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Complete path embeddings in crossed cubes

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INFORMATION SCIENCES 2006年第22期176卷 3332-3346页

作者： Fan, Jianxi Jia, Xiaohua Lin, Xiaola City Univ Hong Kong Dept Comp Sci Kowloon Hong Kong Peoples R China Sun Yat Sen Univ Coll Informat Sci & Technol Guangzhou Peoples R China

Crossed cubes are popular variants of hypercubes. In this paper, we study path embeddings between any two distinct nodes in crossed cubes. We prove two important results in the n-dimensional crossed cube: (a) for any two nodes, all paths whose lengths are greater than or equal to the distance between the two nodes plus 2 can be embedded between the two nodes with dilation 1;(b) for any two integers n >= 2 and l with 1 <= l <= [n+1/2] - 1, there always exist two nodes x and y whose distance is l, such that no path of length l + 1 can be embedded between x and y with dilation 1. The obtained results are optimal in the sense that the dilations of path embeddings are all 1. The results are also complete, because the embeddings of paths of all possible lengths between any two nodes are considered. (C) 2006 Elsevier Inc. All rights reserved.

关键词： interconnection network crossed cube graph embedding optimal embedding parallel computing system

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Large-scale shaking table test and three-dimensional numerical simulation research on earthquake seismic failure response of laterally spreading site-pile group-superstructure system

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BULLETIN OF EARTHQUAKE ENGINEERING 2023年第10期21卷 4789-4819页

作者： Pan, Rujiang Xu, Chengshun Jia, Kemin Dou, Pengfei Kamran, Iqbal Beijing Univ Technol Key Lab Urban Secur & Disaster Engn Minist Educ Beijing 100124 Peoples R China

The method employed in this study combines large-scale shaking table tests with fully coupled 3D non-linear dynamic analysis to investigate the site response and structural damage mechanisms of laterally spreading site cluster pile foundation systems under weak and strong seismic excitation. The study also aims to verify the applicability of the high-efficiency and universal parallel calculation system method, which involves SolidWorks, HyperMesh, OpenSeesMP, and GiD, with a fully visualized interface operation in geotechnical engineering, based on the test database. The results show that under weak seismic excitation, the acceleration and displacement in the free field and near-pile region are linearly distributed along the burial depth, and the motion of shallow pile foundation is mainly controlled by the inertial effect of the superstructure;while under strong seismic excitation, the displacement in the near-field region is much smaller than the free field showing significant pile pinning effect, and the displacement and acceleration in the near-pile domain are cosine-shaped distributed along the burial depth, with the lateral spreading of site liquefaction intensifying. At the intersection of clay and sand layers, a weak interlayer is present, which affects the structural response. The kinematic effect of the site dominates the response, and the location of vulnerability gradually shifts from the pile bottom to the pile head.

关键词： Shaking table test Lateral spreading parallel computing system OpenSeesMP Pile pinning

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Optimal task scheduling algorithm for cyclic synchronous tasks in general multiprocessor networks

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JOURNAL OF parallel AND DISTRIBUTED computing 2005年第3期65卷 261-274页

作者： Park, HJ Kim, BK Korea Adv Inst Sci & Technol Dept Elect Engn & Comp Sci Taejon 305701 South Korea

We develop an optimal task allocation and scheduling algorithm which minimizes the computing period for multiprocessor systems with general network structures considering task execution time and communication contentions and routing delays explicitly. We presented new ideas of scheduling: (i) individual start allowing overlapping two different iterations, (ii) the scheduling space and the scheduling graph representing feasible schedules, and (iii) the check-and-diffusion algorithm utilizing property of the start-time difference vs. the computing period. With concrete examples of scheduling spaces, segments, and scheduled for various multiprocessor network architectures, we showed that individual start reduces the computing period, and our algorithm can find the optimal computing period without exhaustive search. (c) 2004 Elsevier Inc. All rights reserved.

关键词： parallel computing system task allocation and scheduling computing period cyclic synchronous tasks scheduling space

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Edge-pancyclicity and path-embeddability of bijective connection graphs

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INFORMATION SCIENCES 2008年第2期178卷 340-351页

作者： Fan, Jianxi Jia, Xiaohua Qingdao Univ Coll Informat Engn Qingdao 266071 Peoples R China City Univ Hong Kong Dept Comp Sci Hong Kong Hong Kong Peoples R China

An n-dimensional Bijective Connection graph (in brief BC graph) is a regular graph with 2(n) nodes and n2(n-1) edges. The n-dimensional hypercube, crossed cube, Mobius cube, etc. are some examples of the n-dimensional BC graphs. In this paper, we propose a general method to study the edge-pancyclicity and path-embeddability of the BC graphs. First, we prove that a path of length l with dist(X-n, x, y) + 2 <= l <= 2(n) - 1 can be embedded between x and y with dilation 1 in X-n for x,y epsilon V(X-n) with x not equal y in X-n, where X-n (n >= 4) is a n-dimensional BC graph satisfying the three specific conditions and V(X-n) is the node set of X-n. Furthermore, by this result, we can claim that X-n is edge-pancyclic. Lastly, we show that these results can be applied to not only crossed cubes and Mobius cubes, but also other BC graphs except crossed cubes and Mobius cubes. So far, the research on edge-pancyclicity and path-embeddability has been limited in some specific interconnection architectures such as crossed cubes, Mobius cubes. (c) 2007 Elsevier Inc. All rights reserved.

关键词： bijective connection graph crossed cube Mobius cube graph embedding dilation edge-pancyclicity path parallel computing system

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Optimal path embedding in crossed cubes

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IEEE TRANSACTIONS ON parallel AND DISTRIBUTED systemS 2005年第12期16卷 1190-1200页

作者： Fan, JX Lin, XL Jia, XH City Univ Hong Kong Dept Comp Sci Kowloon Hong Kong Peoples R China Sun Yat Sen Univ Coll Informat Sci & Technol Guangzhou Guangdong Peoples R China

The crossed cube is an important variant of the hypercube. The n-dimensional crossed cube has only about half diameter, wide diameter, and fault diameter of those of the n-dimensional hypercube. Embeddings of trees, cycles, shortest paths, and Hamiltonian paths in crossed cubes have been studied in literature. Little work has been done on the embedding of paths except shortest paths, and Hamiltonian paths in crossed cubes. In this paper, we study optimal embedding of paths of different lengths between any two nodes in crossed cubes. We prove that paths of all lengths between [n+1/2] + 1 and 2(n) - 1 can be embedded between any two distinct nodes with a dilation of 1 in the n-dimensional crossed cube. The embedding of paths is optimal in the sense that the dilation of the embedding is 1. We also prove that [n+1/2] - 1 is the shortest possible length that can be embedded between arbitrary two distinct nodes with dilation 1 in the n-dimensional crossed cube.

关键词： crossed cube graph embedding optimal embedding interconnection network parallel computing system

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parallel resultant elimination algorithm to solve the selective harmonic elimination problem

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IET POWER ELECTRONICS 2016年第1期9卷 71-80页

作者： Yang, Kehu Chen, Liangyu Zhang, Jianjun Hao, Jun Yu, Wensheng China Univ Min & Technol Sch Mech Elect & Informat Engn Beijing Peoples R China E China Normal Univ Shanghai Key Lab Trustworthy Comp Shanghai Peoples R China Beijing Univ Posts & Telecommun Sch Elect Engn Beijing Peoples R China

Although the resultant elimination method can get all the possible solutions for the selective harmonic elimination (SHE) problem without the selection of initial values, it still has some fatal shortcomings, such as the high computation burden and the huge memory consumption caused by the intermediate expression swell in the procedure of computing the symbolic determinant of the Sylvester matrix. On the basis of the principle of polynomial interpolation, an algorithm framework is proposed to compute the resultant polynomials, which contains the following two major steps: the evaluation of numerical interpolation points and the solution of linear equations. This approach avoids symbolic computing whose computation complexity is usually very high, furthermore, both of these two steps are suitable for parallel implementing which can speed up the computing tremendously. By using the extended n-dimensional Bjorck-Pereyra's algorithm, this algorithm framework is implemented on a parallel computing system, and it has been used to solve the SHE equations for two-level, three-level, and multilevel inverters. As all the possible solutions can be found by this algorithm, the optimal solutions which have the lowest total harmonic distortion can be identified. Experiment results verify the correctness and effectiveness of the proposed method.

关键词： parallel algorithms matrix algebra interpolation polynomials invertors power engineering computing harmonic distortion parallel resultant elimination algorithm selective harmonic elimination problem Sylvester matrix polynomial interpolation resultant polynomials parallel computing system multilevel inverters three-level inverters two-level inverters harmonic distortion

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