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Multistage Off-Line Permutation Packet Routing on a Mesh: An Approach with Elementary Mathematics

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Abstract

Various methods have been proposed for off-line permutation packet routing on a mesh. One of the methods is known as multistage routing, in which the first stage is crucial. For the first stage of routing, the previous study normally converts it to a problem of graph theory and proves the existence of solutions. However, there is a lack of simple algorithms to the first stage of routing. This article presents an explicit and simple approach for the first stage of routing based on elementary mathematics.

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References

  1. Datta A, Zomaya A Y. An energy-efficient permutation routing protocol for single-hop radio networks. IEEE Transactions on Parallel and Distributed Systems, 2004, 15(4): 331–338.

    Article  Google Scholar 

  2. Liang W, Chen X. Permutation routing in all-optical product networks. IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications, 2002, 49(4): 533–538.

    Article  MathSciNet  Google Scholar 

  3. Leighton F T. Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes. Chapter 1, Morgan Kaufmann Publishers, Inc., USA, 1992.

    Google Scholar 

  4. Symvonis A, Tidswell J. An empirical study of off-line permutation packet routing on two-dimensional meshes based on the multistage routing method. IEEE Transactions on Computers, 1996, 45(5): 619–625.

    Article  MATH  Google Scholar 

  5. Annexstein F, Baumslag M. A unified approach to off-line permutation routing on parallel networks. In Proc. the Second ACM Symposium on Parallel Algorithms and Architectures (SPAA’90), Island of Crete, Greece, July 2–6, 1990, pp.398–406.

  6. Baumslag M, Annexstein F. A unified framework for off-line permutation routing in parallel networks. Mathematical Systems Theory, 1991, 24(4): 233–251.

    Article  MATH  MathSciNet  Google Scholar 

  7. Hall P. On representatives of subsets. Journal of the London Mathematical Society, 1935, 10(1): 26–30.

    Article  MATH  Google Scholar 

  8. Makedon F, Symvonis A. An efficient heuristic for permutation packet routing on meshes with low buffer requirements. IEEE Transactions on Parallel and Distributed Systems, 1993, 3(4): 270–276.

    Article  Google Scholar 

  9. Chlebus B S, Kaufmann M, Sibeyn J F. Deterministic permutation routing on meshes. In Proc. the Fifth ACM Symposium on Parallel and Distributed Processing (SPDP’93), Dallas, TX, USA, December 1–4, 1993, p.284.

  10. Leighton F T, Makedon F, Tollis I G. A 2n − 2 step algorithm for routing in an n × n array with constant size queues. In Proc. the ACM Symposium on Parallel Algorithms and Architectures (SPAA’89), Santa Fe, New Mexico, USA, June 18–21, 1989, pp.328–335.

  11. Rajasekaran S, Overholt R. Constant queue routing on a mesh. Journal of Parallel and Distributed Computing, 1992, 15(2): 160–166.

    Article  MATH  Google Scholar 

  12. Kaklamanis C, Krizanc D, Rao S. Simple path selection for optimal routing on processor arrays. In Proc. the Fourth ACM Symposium on Parallel Algorithms and Architectures (SPAA’92), San Diego, CA, USA, June 29–July 1, 1992, pp.23–30.

  13. Kaufmann M, Sibeyn J F, Suel T. Derandomizing algorithms for routing and sorting on meshes. In Proc. the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, Arlington, VA, USA, Jan 23–25, 1994, pp.669–679.

  14. Krizanc D. A note on off-line routing on a mesh-connected processor array. Parallel Processing Letters, 1991, 1(1): 67–70.

    Article  Google Scholar 

  15. Qiu L. Scheduling and routing of automated guided vehicles [Ph.D. Dissertation]. School of Computer Engineering, Nanyang Technological University, Singapore, 2003.

  16. Cormen T H, Leiserson C E, Rivest R L, Stein C. Introduction to Algorithms. Second Edition, The MIT Press & McGraw-Hill Book Company, 2001.

  17. Chiew K, Qin S. Scheduling and routing of AMOs in an intelligent transport system. IEEE Transactions on Intelligent Transportation Systems, 2008. (to appear)

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  1. School of Information Systems, Singapore Management University, 80 Stamford Road, Singapore, 178902, Singapore

    Kevin Chiew & Yingjiu Li

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  1. Kevin Chiew
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  2. Yingjiu Li
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Correspondence to Kevin Chiew.

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This is the correspondence author who is also known as Ling Qiu under which name the paper was submitted and reviewed.

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Chiew, K., Li, Y. Multistage Off-Line Permutation Packet Routing on a Mesh: An Approach with Elementary Mathematics. J. Comput. Sci. Technol. 24, 175–180 (2009). https://doi.org/10.1007/s11390-009-9203-x

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  • DOI: https://doi.org/10.1007/s11390-009-9203-x

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