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On the theory of interconnection networks for parallel computers

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Automata, Languages and Programming (ICALP 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 820))

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Abstract

Efficient data transfer between processors is an essential component in any large scale parallel computation. Motivated by the growing interest in parallel computers, a significant amount of theoretical research has been devoted to the area of interconnection networks for parallel computers, most of it to the packet routing (or store- and-forward) model of communication. We survey some of the major developments in this field, and discuss several new alternative models of communication, such as wormhole routing, virtual cut-through routing, and hot-potato routing.

Work at the Weizmann Institute supported in part by the Norman D. Cohen Professorial Chair of Computer Science.

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References

  1. B. Aiello, F.T. Leighton, B. Maggs, and M. Newman. Fast algorithms for bit-serial routing on a hypercube. In Proc. of the 2nd Annual ACM Symposium on Parallel Algorithms and Architectures, pages 55–64, 1990.

    Google Scholar 

  2. M. Ajtai, J. Komlós, and E. Szemerédi. Sorting in c log n parallel steps. Combinatorica, 3(1):1–19, 1983.

    Google Scholar 

  3. R. Aleliunas. Randomized parallel communication. In Proc. of the 1st Annual ACM-SIGOPS Symposium on Principles of Distributed Computing, pages 60–72, 1982.

    Google Scholar 

  4. W.C. Athas. Physically compact, high performance multicomputers. In Sixth MIT Conference on Advanced Research in VLSI, pages 302–313, MIT Press, 1990.

    Google Scholar 

  5. A. Bar-Noy, P. Raghavan, B. Schieber, and H. Tamaki. Fast Deflection routing for packets and worms. In Proc. of the 11tn Annual ACM-SIGOPS Symposium on Principles of Distributed Computing, 1993.

    Google Scholar 

  6. A. Borodin and J. E. Hopcroft. Routing, merging, and sorting on parallel models of computation. Journal of Computer and System Sciences, 30:130–145, 1985.

    Google Scholar 

  7. A. Borodin and Y. Rabani. Private communication, 1994.

    Google Scholar 

  8. A. Borodin, P. Raghavan, B. Scheiber, and E. Upfal. How much can hardware help routing? In Proc. of the 25th ACM Symp. on Theory of Computing, pages 573–582, 1993.

    Google Scholar 

  9. H. Chernoff. A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Annals of Math. Stat., 23:493–509, 1952.

    Google Scholar 

  10. W. Dally and C.L. Seitz. Deadlock free message routing in multiprocessor interconnection networks. IEEE Trans. Computers, 36:547–553, 1987.

    Google Scholar 

  11. W.J. Dally. Fine grain message passing concurrent computers. In Third Conference on Hypercube Concurrent Computers and Applications, pages 2–12. ACM Press, 1988.

    Google Scholar 

  12. W.J. Dally. Virtual channel flow control. In Seventeenth Annual International Symposium on Computer Architecture, pages 60–68. ACM Press, 1990.

    Google Scholar 

  13. J. Duato. On the design of deadlock free adaptive routing algorithms for multicomputers: theoretical aspects. In Second European Conference on Distributed Memory Computing, pages 234–243. Springer Verlag LNCS 487, 1991.

    Google Scholar 

  14. S. Felperin, P. Raghavan, and E. Upfal, A theory of wormhole routing in parallel computers. Proceedings of the 33rd Annual IEEE Conference on Foundations of Computer Science, 1992, pages 563–572.

    Google Scholar 

  15. U. Feige and P. Raghavan. Exact analysis of Hot Potato routing. In 33rd Annual Symposium on Foundations of Computer Science, pages 553–562, 1992.

    Google Scholar 

  16. R. I. Greenberg and C. E. Leiserson. Randomized routing on fat-trees. Advances in Computing Research, 5:345–374, 1989.

    Google Scholar 

  17. B. Hajek. Bounds on evacuation time for deflection routing. Distributed Computing, 5:1–6, 1991.

    Google Scholar 

  18. J. Hastad, F.T. Leighton, and M. Newman. Fast computation using faulty hypercube. In Proc. of the 21th Annual ACM Symp. on Theory of Computing, 1989, pages 251–263.

    Google Scholar 

  19. W. Hoeffding. On the distribution of the number of successes in independent trails. Ann. of Math. Stat. 27:713–721, 1958.

    Google Scholar 

  20. C. Kaklamanis, D. Krizanc, and S. Rao. Improved hot potato routing for processor array. In Proc. of the 5rd Annual ACM Symposium on Parallel Algorithms and Architectures, pages 273–282, 1993.

    Google Scholar 

  21. C. Kaklamanis, D. Krizanc, and T. Tsantilas. Tight bounds for oblivious routing in the hypercube. In Proc. of the 3rd Annual ACM Symposium on Parallel Algorithms and Architectures, pages 31–36, 1991.

    Google Scholar 

  22. F.T. Leighton. Tight bounds on the complexity of parallel sorting. IEEE Transactions on Computers, C-34:344–354, 1985.

    Google Scholar 

  23. F.T. Leighton. Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes. Morgan Kaufmann Publishers, San Mateo, California 1992.

    Google Scholar 

  24. F.T. Leighton. Average case analysis of greedy routing algorithms on arrays. In Second Annual ACM Symposium on Parallel Algorithms and Architectures, pages 2–10. 1990.

    Google Scholar 

  25. F.T. Leighton. Methods for Message Routing in Parallel Machines. In Proc. of the 24th Annual ACM Symp. on Theory of Computing, 1992, pages 77–96.

    Google Scholar 

  26. F.T. Leighton and B. Maggs. Expanders might be practical: Fast algorithms for routing around faults in multibutterflies. In Proc. of the 30th Annual Symposium on Foundations of Computer Science, pages 384–389, 1989.

    Google Scholar 

  27. C. E. Leiserson. Fat-trees: universal networks for hardware-efficient supercomputing. IEEE Transactions on Computers, C-34(l0):892–901, 1985.

    Google Scholar 

  28. C. E. Leiserson. VLSI theory and parallel supercomputing. In R.F. Rashid, editor, Carnegie Mellon University School of Computer Science 25th Ann. Symp. Addison-Wesley, 1991. Pages 29–44.

    Google Scholar 

  29. A. Lubotzky, R. Phillips, and P. Sarnak. Ramanujan graphs. Combinatorica, 8(3):261–277, 1988.

    Google Scholar 

  30. Y.-D. Lyuu. Fast fault-tolerance parallel communication and on-line maintenance using information disposal. In Second Annual ACM Symposium on Parallel Algorithms and Architectures, pages 378–387, 1990

    Google Scholar 

  31. F. Makedon and A. Simvonis. On bit-serial packet routing for the mesh and the torus. In Third Symposium on Frontiers of Massively Parallel Computation, pages 294–302. IEEE Computer Society Press, 1990.

    Google Scholar 

  32. I. Newman and A. Schuster. Hot potato algorithms for permutation routing. Technical Report, PCL Report # 9201, CS dept., Technion, November 1992.

    Google Scholar 

  33. I. Newman and A. Schuster. Hot-potato worm routing via store-and forward packet routing. In Proc. 2nd Israeli Symp. on Theory of Computing and Systems, 1993.

    Google Scholar 

  34. M. Noakes and W.J. Dally. System design of the j machine. In Sixth MIT Conference on Advanced Research in VLSI, pages 179–194. MIT Press, 1990.

    Google Scholar 

  35. D. Peleg and E. Upfal. Time-randomness trade-off for oblivious routing. SIAM Journal on Computing, 19:256–266, 1990.

    Google Scholar 

  36. N. Pippenger. Parallel communication with limited buffers. In 25th Annual Symposium on Foundations of Computer Science, pages 127–136, 1984.

    Google Scholar 

  37. N. Pippenger. Communication networks. In J. Van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity. MIT Press, Cambridge, 1990, pages 805–834.

    Google Scholar 

  38. F. Preparata. Holographic dispersal and recovery of information. IEEE Trans. Information Theory, IT-35(5):1123–1124, 1989.

    Google Scholar 

  39. M. Rabin. Efficient dispersal of information for security, load balancing, and fault tolerance. Journal of the ACM, 36(2):335–348, 1989.

    Google Scholar 

  40. A. Ranade. How to emulate shared memory. In Proceedings of the 28th Annual IEEE Symposium on Foundations of Computer Science, pages 185–194, 1987.

    Google Scholar 

  41. E. Upfal. Efficient schemes for parallel communication. Journal of the ACM, 31:507–517, 1984. (Preliminary version in PODC 82.)

    Google Scholar 

  42. E. Upfal. An O(log N) deterministic packet routing scheme. Journal of the ACM, pages 55–70, 1992. (Preliminary version in STOC 1989.)

    Google Scholar 

  43. L.G. Valiant. A scheme for fast parallel communication. SIAM Journal on Computing, 11(2):350–361, 1982.

    Google Scholar 

  44. L.G. Valiant. General purpose parallel architectures. In J. Van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity. MIT Press, Cambridge, 1990, pages 943–972.

    Google Scholar 

  45. L. G. Valiant and G. J. Brebner. Universal schemes for parallel communication. In Proc. of the 13th Annual ACM Symposium on Theory of Computing, pages 263–277, 1981.

    Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel

    Eli Upfal

  2. IBM Almaden Research Center, San Jose, California

    Eli Upfal

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  1. Eli Upfal
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Serge Abiteboul Eli Shamir

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© 1994 Springer-Verlag Berlin Heidelberg

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Upfal, E. (1994). On the theory of interconnection networks for parallel computers. In: Abiteboul, S., Shamir, E. (eds) Automata, Languages and Programming. ICALP 1994. Lecture Notes in Computer Science, vol 820. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58201-0_91

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  • DOI: https://doi.org/10.1007/3-540-58201-0_91

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58201-4

  • Online ISBN: 978-3-540-48566-7

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