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Design and analysis of the Dual-Torus Network

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Abstract

In this paper, we propose a new topology called theDual Torus Network (DTN) which is constructed by adding interleaved edges to a torus. The DTN has many advantages over meshes and tori such as better extendibility, smaller diameter, higher bisection width, and robust link connectivity. The most important property of the DTN is that it can be partitioned into sub-tori of different sizes. This is not possible for mesh and torus-based systems.

The DTN is investigated with respect to allocation, embedding, and fault-tolerant embedding. It is shown that the sub-torus allocation problem in the DTN reduces to the sub-mesh allocation problem in the torus. With respect to embedding, it is shown that a topology that can be embedded into a mesh with dilation δ can also be embedded into the DTN with less dilation. In fault-tolerant embedding, a fault-tolerant embedding method based on rotation, column insertion, and column skip is proposed. This method can embed any rectangular grid into its optimal square DTN when the number of faulty nodes is fewer than the number of unused nodes. In conclusion, the DTN is a scalable topology well-suited for massively parallel computation.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Pohang University of Science and Technology (POSTECH), San 31 Hyoja Dong, 790-784, Pohang, South Korea

    SangHo Chae, Jong Kim & SungJe Hong

  2. Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), San 31 Hyoja Dong, 790-784, Pohang, South Korea

    Sunggu Lee

Authors
  1. SangHo Chae
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  2. Jong Kim
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  3. SungJe Hong
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  4. Sunggu Lee
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Additional information

Sang-Ho Chae, M.S.: He received the B.S. in the Computer Science and Engineering from the Pohang University of Science and Technology (POSTECH) in 1994, and the M.E. in 1996. Since 1996, he works as an Associate Research Engineer in the Central R&D Center of the SK Telecom Co. Ltd. He took part in developing SK Telecom Short Message Server whose subscribers are now over 3.5 million and Advanced Paging System in which he designed and implemented high availability concepts. His research interests are the Fault Tolerance, Parallel Processing, and Parallel Topolgies.

Jong Kim, Ph.D.: He received the B.S. degree in Electronic Engineering from Hanyang University, Seoul, Korea, in 1981, the M.S. degree in Computer Science from the Korea Advanced Institute of Science and Technology, Seoul, Korea, in 1983, and the Ph.D. degree in Computer Engineering from Pennsylvania State University, U.S.A., in 1991. He is currently an Associate Professor in the Department of Computer Science and Engineering, Pohang University of Science and Technology, Pohang, Korea. Prior to this appointment, he was a research fellow in the Real-Time Computing Laboratory of the Department of Electrical Engineering and Computer Science at the University of Michigan from 1991 to 1992. From 1983 to 1986, he was a System Engineer in the Korea Securities Computer Corporation, Seoul, Korea. His major areas of interest are Fault-Tolerant Computing, Performance Evaluation, and Parallel and Distributed Computing.

Sung Je Hong, Ph.D.: He received the B.S. degree in Electronics Engineering from Seoul National University, Korea, in 1973, the M.S. degree in Computer Science from Iowa State University, Ames, U.S.A., in 1979, and the Ph.D. degree in Computer Science from the University of Illinois, Urbana, U.S.A., in 1983. He is currently a Professor in the Department of Computer Science and Engineering, Pohang University of Science and Technology, Pohang, Korea. From 1983 to 1989, he was a staff member of Corporate Research and Development, General Electric Company, Schenectady, NY, U.S.A. From 1975 to 1976, he was with Oriental Computer Engineering, Korea, as a Logic Design Engineer. His current research interest includes VLSI Design, CAD Algorithms, Testing, and Parallel Processing.

Sunggu Lee, Ph.D.: He received the B.S.E.E. degree with highest distinction from the University of Kansas, Lawrence, in 1985 and the M.S.E. and Ph.D. degrees from the University of Michigan, Ann Arbor, in 1987 and 1990, respectively. He is currently an Associate Professor in the Department of Electronic and Electrical Engineering at the Pohang University of Science and Technology (POSTECH), Pohang, Korea. Prior to this appointment, he was an Associate Professor in the Department of Electrical Engineering at the University of Delaware in Newark, Delaware, U.S.A. From June 1997 to July 1998, he spent one year as a Visiting Scientist at the IBM T. J. Watson Research Center. His research interests are in Parallel, Distributed, and Fault-Tolerant Computing. Currently, his main research focus is on the high-level and low-level aspects of Inter-Processor Communications for Parallel Computers.

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Chae, S., Kim, J., Hong, S. et al. Design and analysis of the Dual-Torus Network. NGCO 17, 229–254 (1999). https://doi.org/10.1007/BF03037221

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  • DOI: https://doi.org/10.1007/BF03037221

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