Abstract
We describe a methodology for constructing parallel algorithms that are transportable among parallel computers having different numbers of processors, different bandwidths of interprocessor communication and different periodicity of global synchronisation. We do this for the bulk-synchronous parallel (BSP) model, which abstracts the characteristics of a parallel machine into three numerical parameters p, g, and L, corresponding to processors, bandwidth, and periodicity respectively. The model differentiates memory that is local to a processor from that which is not, but, for the sake of universality, does not differentiate network proximity. The advantages of this model in supporting shared memory or PRAM style programming have been treated elsewhere. Here we emphasise the viability of an alternative direct style of programming where, for the sake of efficiency the programmer retains control of memory allocation. We show that optimality to within a multiplicative factor close to one can be achieved for the problems of Gauss-Jordan elimination and sorting, by transportable algorithms that can be applied for a wide range of values of the parameters p, g, and L. We also give some simulation results for PRAMs on the BSP to identify the level of slack at which corresponding efficiencies can be approached by shared memory simulations, provided the bandwidth parameter g is good enough.
This research was supported in part by the National Science Foundation under grant CCR-89-02500 and by the Office of Naval Research under grant N00014-85-K-0445.
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References
R. Aleliunas. Randomized parallel computation. In ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pages 60–72, August 1982.
Richard J. Anderson and Gary L. Miller. Optical communication for pointer based algorithms. Technical Report CRI 88-14, 1988.
D. Angluin and L. G. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. J. Computer and System Sciences, 18:155–193, 1979.
Martin Dietzfelbinger and Friedhelm Meyer auf der Heide. A new universal class of hash functions and dynamic hashing in real time. International Colloqium on Automata, Languages and Programming, 443:6–19, 1990.
G. C. Fox, M. A. Johnson, G. A. Lyzenga, S. W. Otto, J. K. Salmon, and D. W. Walker. Solving Problems on Concurrent Processors, Vol 1: General Techniques and Regular Problems. Prentice Hall, Englewood Cliffs, New Jersey, 1988.
W. D. Frazer and A. C. McKellar. Samplesort: A sampling approach to minimal storage tree sorting. Journal of the ACM, 17:3:496–507, 1970.
Alfred Hartmann and Steve Redfield. Design sketches for optical crossbar switches intended for large scale parallel processing applications. Optical Engineering, 29:3:315–327, April 1989.
C. A. R. Hoare. Quicksort. Computer Journal, 5:10–15, 1962.
J. S. Huang and Y. C. Chow. Parallel sorting and data partitioning by sampling. IEEE Computer Society's Seventh International Computer Software and Applications Conference, pages 627–631, November 1983.
V. F. Kolchin, B. A. Sevastyanov, and V. P. Chistyakov. Random Allocations. Translation ed. A. V. Balakrsishnan, Halsted Press, 1978.
Richard A. Linke. Power distribution in a planar-waveguide based broadcast star network. IEEE Photonics Technology Letters, 3:9:850–852, September 1991.
Eric S. Maniloff, Kristina M. Johnson, and J. H. Reif. Holographic routing network for parallel processing machines. In Holographic Optics II: Principles and Applications, Proc. SPIE (G. M. Morris, ed.), 1136:283–289, 1989.
D. Nassimi and S. Sahni. Parallel permutation and sorting algorithms and a new generalized connection network. Journal of the ACM, 29:3:642:667, July 1982.
J. H. Reif and L. G. Valiant. A logarithmic time sort for linear size networks. Journal of the ACM, 34:60–76, January 1987.
E. Upfal. Efficient schemes for parallel communication. In ACM SIGACTSIGOPS Symposium on Principles of Distributed Computing, pages 55–59, August 1982.
L. G. Valiant. General purpose parallel architectures. In Handbook of Theoretical Computer Science (J. van Leeuwen, ed.), North Holland, pages 945–971, 1990.
L. G. Valiant. A bridging model for parallel computation. Communications of the ACM, 33:103–111, August 1990.
M. H. van Emden. Increasing the efficiency of quicksort. Communications of the ACM, 13:9:563–567, 1970.
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© 1992 Springer-Verlag Berlin Heidelberg
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Gerbessiotis, A.V., Valiant, L.G. (1992). Direct bulk-synchronous parallel algorithms. In: Nurmi, O., Ukkonen, E. (eds) Algorithm Theory — SWAT '92. SWAT 1992. Lecture Notes in Computer Science, vol 621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55706-7_1
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DOI: https://doi.org/10.1007/3-540-55706-7_1
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