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Randomized Algorithms on the Mesh

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Book cover Advances in Randomized Parallel Computing

Part of the book series: Combinatorial Optimization ((COOP,volume 5))

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Abstract

The mesh-connected array is an attractive architecture for parallel machines, and a number of existing parallel machines are based on a mesh topology. In this paper, we survey the results on three fundamental problems in parallel computation: routing, sorting, and selection, and demonstrate that randomized algorithms are the most natural and efficient algorithms available for many different variants of these problems on the mesh.

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References

  1. T. Blank. The Maspar MP-1 architecture. In Proceedings of IEEE Compcon, 1990.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. H. Chernoff. A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Annals of Mathematics and Statistics, 23: 493–507, 1952.

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Condon and L. Narayanan. Upper and lower bounds for selection on the mesh. In Symposium on Parallel and Distributed Processing. pages 497–504. IEEE, 1994.

    Google Scholar 

  5. I. Corporation. Paragon XP/S product overview. Technical report, Intel, 1991.

    Google Scholar 

  6. T. Dachraoui and L. Narayanan. Fast deterministic sorting on large parallel machines. In Symposium on Parallel and Distributed Processing. IEEE, 1996. To appear.

    Google Scholar 

  7. W. Dally. Wire efficient VLSI multi-processor communication networks. In Advanced Research in Advanced Research in VLSI, pages 391–415, 1987.

    Google Scholar 

  8. R. Diekmann, J. Gehring, R. Luling, B. Monien, M. Nubel, and R. Wanka. Sorting large data sets on a massively parallel system. In Proceedings of the Symposium on Parallel and Distributed Processing, pages 2–9. IEEE, 1994.

    Google Scholar 

  9. U. Feige and P. Raghavan. Exact analysis of hot-potato routing. In Symposium on the Foundations of Computer Science, pages 553–562. IEEE, 1992.

    Google Scholar 

  10. S. Felperin, P. Raghavan, and E. Upfal. A theory of wormhole routing in parallel computers. In Symposium on the Foundations of Computer Science, pages 563–572. IEEE, 1992.

    Google Scholar 

  11. R. Floyd and R. Rivest. Expected time bounds for selection. Communications of the ACM, 18: 165–172, 1975.

    Article  MATH  Google Scholar 

  12. W. Hightower, J. Prins, and J. Reif. Implementations of randomized sorting on large parallel machines. In Symposium on Parallel Algorithms and Architecture, pages 158–167. ACM, 1992.

    Google Scholar 

  13. C. Kakalamanis and D. Krizanc. Optimal sorting on mesh-connected processor arrays. In Symposium on Parallel Algorithms and Architecture, pages 50–59, 1992.

    Google Scholar 

  14. C. Kaklamanis and D. Krizanc. Multipacket hot-potato routing on processor arrays. In Euro-Par, pages 270–277, 1996.

    Google Scholar 

  15. C. Kaklamanis, D. Krizanc, L. Narayanan, and A. Tsantilas. Randomized sorting and selection on mesh-connected processor arrays. In Symposium on Parallel Algorithms and Architecture, pages 17–28, 1991.

    Google Scholar 

  16. C. Kaklamanis, D. Krizanc, and S. Rao. Simple path selection for optimal routing on processor arrays. In Symposium on Parallel Algorithms and Architecture, pages 23–30, 1992.

    Google Scholar 

  17. C. Kaklamanis, D. Krizanc, and S. Rao. Hot-potato routing on processor arrays. In Symposium on Parallel Algorithms and Architecture, pages 273– 282, 1993.

    Google Scholar 

  18. C. Kaklamanis, D. Krizanc, and A. Tsantilas. Tight bounds for oblivious routing in the hypercube. In Symposium on Parallel Algorithms and Architecture, pages 31–36, 1990.

    Google Scholar 

  19. M. Kaufmann, S. Rajasekaran, and J. Sibeyn. Matching the bisection bounds for routing and sorting on the mesh. In Proceedings of SPAA 92, pages 31–40, 1992.

    Chapter  Google Scholar 

  20. M. Kaufmann, J. Sibeyn, and T. Suel. Derandomizing algorithms for routing and sorting on meshes. In Symposium on Discrete Algorithms, pages 669–679. ACM-SIAM, 1994.

    Google Scholar 

  21. M. Kaufmann, J. Sibeyn, and T. Suel. Beyond the bisection bound: ranking and counting on meshes. In Proceedings of the European Symposium on Algorithms, volume LNCS 979, 1995.

    Google Scholar 

  22. D. Krizanc and L. Narayanan. Optimal algorithms for selection on a mesh-connected processor array. In Symposium on Parallel and Distributed Processing, pages 70–76. IEEE, 1992.

    Google Scholar 

  23. D. Krizanc, L. Narayanan, and R. Raman. Fast deterministic selection on mesh-connected processor arrays. Algorithmica, 15: 319–332, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  24. M. Kunde. 1-selection and related problems on grids of processors. Journal of New Generation Computer Systems, 2: 129–143, 1989.

    MathSciNet  Google Scholar 

  25. M. Kunde. Concentrated regular data streams on grids: Sorting and routing near to the bisection bound. In Symposium on the Foundations of Computer Science, pages 141–150. IEEE, 1991.

    Google Scholar 

  26. M. Kunde. Block gossiping on grids and tori: Sorting and routing match the bisection bound deterministically. In Proceedings of the 1st European Symposium on Algorithms, 1993.

    Google Scholar 

  27. F. Leighton, F. Makedon, and I. Tollis. A 2n-2 step algorithm for routing in an r x n array with constant size queues. In Symposium on Parallel Algorithms and Architecture, pages 328–335, 1989.

    Google Scholar 

  28. F. T. Leighton. Average case analysis of greedy routing algorithms on arrays. In Symposium on Parallel Algorithms and Architecture, pages 2–10, 1990.

    Google Scholar 

  29. F. T. Leighton. Introduction to Parallel Algorithms and Architectures: Arrays, Trees and Hypercubes. Morgan Kaufmann, 1992.

    Google Scholar 

  30. F. T. Leighton. Methods for message routing in parallel computers. In Symposium on the Theory of Computation, pages 77–96, 1992.

    Google Scholar 

  31. F. Meyer auf der Heide and M. Westermann. Hot-potato routing on multi-dimensional tori. In Work-shop on Graph-Theoretic Concepts in Computer Science, pages 275–287, 1995.

    Google Scholar 

  32. L. Narayanan. Selection, Sorting, and Routing on Mesh-Connected Processor Arrays. PhD thesis, University of Rochester, 1992.

    Google Scholar 

  33. M. Noakes, D. Wallach, and W. Dally. The J-machine multicomputer: an architectural evaluation. In International Symposium on Computer Architecture, 1993.

    Google Scholar 

  34. S. Rajasekaran. k - k routing, k - k sorting and cut-through routing on the mesh. Journal of Algorithms, 19: 361–382, 1995.

    Article  MathSciNet  Google Scholar 

  35. S. Rajasekaran, W. Chen, and S. Yooseph. Unifying themes for network selection. In Proceedings of ISSAC, 1995.

    Google Scholar 

  36. S. Rajasekaran and Overholt. Constant queue routing on a mesh. In Symposium on Theoretical Aspects of Computer Science, pages 444–455, 1991.

    Google Scholar 

  37. S. Rajasekaran and T. Tsantilas. Optimal algorithms for routing on the mesh. Algorithmica, 8: 21–38, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  38. J. Reif and L. Valiant. A logarithmic time sort for linear size networks. Journal of the ACM, 34 (l): 60–76, 1987.

    Article  MathSciNet  Google Scholar 

  39. R. Reischuk. Probabilistic parallel algorithms for sorting and selection. SIAM Journal of Computing, 14 (2): 396–411, May 1985.

    Article  MathSciNet  MATH  Google Scholar 

  40. C. Schnorr and A. Shamir. An optimal sorting algorithm for mesh-connected computers. In Symposium on the Theory of Computation, pages 255–263, 1986.

    Google Scholar 

  41. W. Seitz, C., Athas, F. C., A. Martin, J. Siezovic, C. Steele, and W. Su. The architecture and programming of the ametek series 20101 multicomputer. In Proceedings of the Third Conference on Hypercube Concurrent Computers and Applications, pages 33–36, 1988.

    Google Scholar 

  42. C. Thompson and H. Kung. Sorting on a mesh connected parallel computer. Communications of the ACM, 20: 263–270, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  43. L. Valiant. A scheme for fast parallel communication. SIAM Journal of Computing, 11: 350–361, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  44. L. Valiant and G. Brebner. Universal schemes for parallel communication. In Symposium on the Theory of Computation, pages 263–277. 1981.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Concordia University, Montreal, Quebec, H3H 1G7, Canada

    Lata Narayanan

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  1. Lata Narayanan
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Editor information

Editors and Affiliations

  1. University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos  & Sanguthevar Rajasekaran  & 

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© 1999 Kluwer Academic Publishers

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Narayanan, L. (1999). Randomized Algorithms on the Mesh. In: Pardalos, P.M., Rajasekaran, S. (eds) Advances in Randomized Parallel Computing. Combinatorial Optimization, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3282-4_4

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  • DOI: https://doi.org/10.1007/978-1-4613-3282-4_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3284-8

  • Online ISBN: 978-1-4613-3282-4

  • eBook Packages: Springer Book Archive

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