# Correlation of Algorithms, Software and Hardware of Parallel Computers

## Abstract

In the past, the speed of computers was mainly increased by increasing the speed of their logic element. Thus, the memory cycle time has increased by two orders of magnitude. Improvements in technology achieved in the last 20 years have increased the speed of processors by as much as three orders. Today, since the physical barrier of the speed of transfer of an electric signal has been reached, it is possible to achieve additional speed only by improving the computer organization or by using it more effectively. Current technology has made it possible for the processors to be combined into large parallel structures, and by a suitable organization of *n* processors it is possible to reach an *n*-fold increase in the rate of computation. Parallelism in computation has brought with it new problems both in the creation of new algorithms and programs, and in the design of computer architectures. Parallel algorithms and programs are closely connected with the architecture of parallel computers, and therefore design and analysis of parallel algorithms and programs cannot be considered independently of their implementation and the architecture of the computer on which they are to be implemented. Several examples are known from the history of parallel data processing, where a valuable concept in the design of algorithms, programs or computers has had a large impact on the efficiency of computation.

### Keywords

Neral Radar Convolution Sorting Akron## Preview

Unable to display preview. Download preview PDF.

### References

- [1]Baer, J. L.: Survey of some theoretical aspects of multiprocessing. Comp. Surveys.
*5*, 1973, 1. 31–80MATHCrossRefGoogle Scholar - [2]Barnes, G. et al.: The ILLIAC IV computer. IEEE Trans. on Computers,
*C-1*7, 1968, 746–757.Google Scholar - [3]Batcher, K. E.: Sorting networks and their applications. Spring Joint Comp. Conf., 1968, AFIPS Proc., 32. Thompson, Washington, 1968, pp. 307–314.Google Scholar
- [4]Chon, S. CH. and Kuck, D. J.: Time and parallel processor bounds for linear recurrence systems. IEEE Trans. on Computers,
*C-24*, 1975, 701–717.Google Scholar - [5]Control Data Corporation, STAR-100 Computer Hardware Reference Manual, 1974.Google Scholar
- [6]Conway, M. E.: A multiprocessor system design. AFIPS Conf. Proc. 1963, FJCC 24. Spartan Books, Baltimore, 1963, pp. 139–146.Google Scholar
- [7]Dijkstra, E. W.: Cooperating sequential processes. In: Programming Languages. F Genuys (Editor). Academic Press, New York, 1968. pp. 43–1122.Google Scholar
- [8]Duff, M. J. and Watson, D.: A parallel computer for array processing. Proc. IFIP Congress, North-Holland Publ. Co., Amsterdam, 1975, pp. 94–99.Google Scholar
- [9]Enslow. P.. Jr. (Editor): Multiprocessors and Parallel Processing. Willey—Intel—science, New York, 1974.MATHGoogle Scholar
- [10]Flanders, P. M. et al.: Efficient high-speed computing with the distributed array processor. In: High-Speed Computers and Algorithms Organization. D. J. Kuck. D. H. Lawrio and A H. Sameh (Editors). Academic Press, New York, 1977. pp. 113–128.Google Scholar
- [1l]Flynn, M. J.: Toward more efficient computer organizations. Proc. Spring Joint Comp Conf.. AFIPS Press, 1972, pp. 1211–1217.Google Scholar
- [12]Gentleman. W. M.: Some complexity results for matrix computations on parallel processors. J. ACM,
*25*, 1978, 1. 112–115.MathSciNetMATHCrossRefGoogle Scholar - [13]Graham, R. L.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math..
*17*. 1999, 2. 416–429.Google Scholar - [14]Ihnat, J. P. et al.: The use of two levels of parallelism to implement an efficient programmable signal processing computer. Sagamore Comp. Conf. on Parallel Processing, Sagamore, 1973, pp. 113–119.Google Scholar
- [15]Keck. D.: ILLIAC IV software and application programming. IEEE Trans. on Computers.
*C-17*. 1968. 8, 758–770.CrossRefGoogle Scholar - [16]Kuck, D.: Multioperation machine computational complexity. In: Complexity of Sequential and Parallel Numerical Algorithms. J. F. Traub (Editor). Academic Press. New York. 1973. pp. 17–47.Google Scholar
- [17]Kung. H. T.: Synchronized and asynchronous parallel algorithms for multiprocessors. In: Algorithms and Complexity. J. F. Traub (Editor). Academic Press. New York. 1976. pp. 153–200.Google Scholar
- [18]Lambiotto, J. J. and Voigt, R. G.: The solution of tridiagonal systems of equations on the CDC STAR-100 computer. ACM Trans. on Math. Software,
*1*, 1975, 4, 308–329.MathSciNetCrossRefGoogle Scholar - [19]Lawrie, D. H. et al.: GLYPNIR–a programming language for ILLIAC IV. Comm. CAC.
*15*. 1975, 3, 157–164.CrossRefGoogle Scholar - [20]Madsen. N. K. et al.: Matrix multiplication by diagonals on a vector parallel processor. Inform. Proc. Lett.,
*5*, 1976, 2, 41–45.MathSciNetMATHCrossRefGoogle Scholar - [21]Mirenkov, N. N.: Strukturnoe parallelnoe programmirovanie. Programmirovanie.
*3*. 1975. 3–14.MathSciNetGoogle Scholar - [22]Owens, J. L.: The influence of machine organization on algorithms. In: Complexity of Sequential and Parallel Numerical Algorithms. J. F. Traub (Editor). Academic Press, New York, 1973, pp. 111–130.Google Scholar
- [23]Raj Reddy. D.: Some numerical problems in artificial intelligence: Implications for complexity and machine architecture. In: Complexity of Sequential and Parallel Numerical Algorithms. J. F. Traub (Editor). Academic Press, New York. 1973, pp. 131–147.Google Scholar
- [24]Sl Aran: System description. A new class of computer. Goodyear Aerospace Corp.. Akron. Ohio, 1974.Google Scholar
- [25]Stone, H. S.: Parallel processing with perfect schuffle. IEEE Trans. on Computers,
*C-20*, 1971, 2. 153–161.CrossRefGoogle Scholar - [26]Stone, H. S.: Parallel tridiagonal equation solver. ACM Trans. on Math. Software,
*1*. 1975, 289–307.MATHCrossRefGoogle Scholar - [27]Stone, H. S. (Editor): Introduction to Computer Architecture. Sci. Res. Assoc., Inc., Chicago, 1975.Google Scholar
- [28]Stone. H. S.: An efficient parallel algorithm for the solution of a tridiagonal system of equations. J. ACM,
*20*. 1973, 27–30.MATHCrossRefGoogle Scholar - [29]Swan, R. J. et al.: The structure and architecture of CM*: A modular multiprocessor. Tech. Report, Dep. Comp. Sci., Carnegie-Mellon Univ., Pittsburg, 1977.Google Scholar
- [30]Shakhbazyan, K. V. and Tushkina, T. A.: Obzor metodov sostavleniya raspisanii dls’a mnogoprotsessornykh sistem. Zap. nauch. semin. LOMI, AN SSSR, Leningrad, 5-I. 1975. pp. 229–258.Google Scholar
- [31]Thompson, C. D.: Generalized connection networks for parallel processor intercommunication. Tech. Report, Dep. Comp. Sci., Carnegie-Mellon Univ., Pittsburg, 1977.Google Scholar
- [32]Thurber, K. J.: Large scale computer architecture. In: Parallel and Associative Processors. Hayden Book Co., Rochello Part, N. J., 1976.Google Scholar
- [33]Tutle, P. G.: Implementation of selected eigenvalue algorithms on a vector computer. Tech. Report NPGD-TM-330, Babcock and Wilcox 1975.Google Scholar
- [34]Vairavan, K. and Demilt.o, R. A.: On the computational complexity of a generalized scheduling problem. IEEE Trans. on Computers,
*C-25*, 1976, 11, 1067–1073.MathSciNetCrossRefGoogle Scholar - [35]Wulf, W. A. and Bell, C. G.: C mmp — a multi-miniprocessor. AFIPS Conf. Proc. 1972, FJCC 41. AFIPS Press, Montwale, N. J., pp. 765–777.Google Scholar
- [1]Stone, H. S.: Parallel processing with the perfect shuffle. IEEE Trans. on Computers.
*C-20*. 1971, 2, 153–161.CrossRefGoogle Scholar - [2]Fixo, B. J. and Algazi, V. R.: A unified treatment of discrete fast unitary transforms. SIAM J. Computing,
*6*, 1977, 4, 700–717.Google Scholar - [3]Batcher, K. E.: Sorting networks and their applications. Spring Joint Computer Conf. AFIPS Proc., Vol. 32. Thompson, Washington, D. C., 1968, pp. 307–314.Google Scholar
- [4]Brigham, E. O.: The Fast Fourier Transform. Prentice Hall, Englewood Cliffs. N. J., 1974.MATHGoogle Scholar
- [5]Clos, C.: A study of non-blocking switching networks. Bell Syst. Tech. J.,
*32*, 1953, 406–424.Google Scholar