skip to main content
article
Open Access

Ultracomputers

Authors Info & Claims
Published:01 October 1980Publication History
Skip Abstract Section

Abstract

A class of parallel processors potentially involving thousands of individual processing elements is described. The architecture is based on the perfect shuffle connection and has two favorable characteristics: (1) Each processor communicates with a fixed number of other processors. (2) Important communication functions can be accomplished in time proportional to the logarithm of the number of processors. A number of basic algorithms for these “ultracomputers” are presented, and physical design considerations are discussed in a preliminary fashion.

References

  1. 1 AHO, A., HOPCROFT, J., AND ULLMAN, J.D. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Mass., 1976.]] Google ScholarGoogle Scholar
  2. 2 BATCHER, K.E. Sorting networks and their applications. Proc. 1968 Spring JCC, AFIPS Press, Arlington, Va., pp. 307-314.]]Google ScholarGoogle Scholar
  3. 3 BAUDET, G., AND STEVENSOn, D. Optimal sorting algorithms for parallel computers. Tech. Rep., Computer Science Dep., Carnegie-Mellon Univ., Pittsburgh, Pa. See also IEEE Trans. Comput. C-27 (1978), 84-86.]]Google ScholarGoogle Scholar
  4. 4 BE~ES, V.E. Mathematical theory of connecting networks and telephone traffic. Academic Press, New York, 1965.]]Google ScholarGoogle Scholar
  5. 5 CHANORA, A.K. Maximal parallelism in matrix multiplication. Rep. RC-6193, IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y., 1976.]]Google ScholarGoogle Scholar
  6. 6 CLOS, C. A study of nonblocking switching networks. Bell Syst. Tech. J. 32 (1953), 406-424.]]Google ScholarGoogle Scholar
  7. 7 CSANKY, L. Fast parallel matrix inversion algorithms. SIAM J. Cornput. 5 (1976), 618-623. See also Proc. 16th Ann. IEEE Syrup. on Foundations of Computer Science, Berkeley, Calif., 1975, pp. 11-12.]]Google ScholarGoogle Scholar
  8. 8 GOTrLIEB, A. PLUS--A PL/I ultracomputer simulator, I. Ultracomputer Note, Computer Science Dep., New York Univ., New York, N.Y., 1980.]]Google ScholarGoogle Scholar
  9. 9 GOTTLIEB, A. PLUS--A PL/I ultracomputer simulator, II. Ultracomputer Note, Computer Science Dep., New York Univ., New York, N.Y., 1980.]]Google ScholarGoogle Scholar
  10. 10 GOTTLIEB, A., AND KRUSKAL, C.P. MULT--A multitasking ultracomputer language with timing, I. Ultracomputer Note, Computer Science Dep., New York Univ., New York, N.Y., 1980.]]Google ScholarGoogle Scholar
  11. 11 GOTTLIEB, A., AND KRUSKAL, C.P. MULT--A multitasking ultracomputer language with timing, xl 28II. Ultracomputer Note, Computer Science Dep., New York Univ., New York, N.Y., 1980. II. Ultracomputer Note, Computer Science Dep., New York Univ., New York, N.Y., 1980.]]Google ScholarGoogle Scholar
  12. 12 GOTTLIEB, A., AND KRUSKAL, C.P. Supersaturated ultracomputer algorithms. Ultracomputer Note, Computer Science Dep., New York Univ., New York, N.Y., 1980.]]Google ScholarGoogle Scholar
  13. 13 HmSHBERC, D.S. Parallel algorithms for the transitive closure and the connected component problems. Proc. 8th Ann. ACM Symp. on Theory of Computing, Hershey, Pa., May 1976, pp. 55- 57.]] Google ScholarGoogle Scholar
  14. 14 HmSCHBERG, D.S. Fast parallel sorting algorithms. Commun. ACM 21, 8 (Aug. 1978), 657-661. See also Tech. Rep., Dep. of Electrical Engineering, Rice Univ., Houston, Texas, 1977.]] Google ScholarGoogle Scholar
  15. 15 KNU?H, D.E. The Art of Computer Programming, Vol. 3: Sorting and Searching. Addison- Wesley, Reading, Mass., 1972, pp. 232-235.]]Google ScholarGoogle Scholar
  16. 16 KUNG, H.T. New algorithms and lower bounds for the parallel evaluation of certain rational expressions and recurrences. J. ACM 23, 2 (April 1979), 252-261. See also Proc. 6th Ann. ACM Symp. on Theory of Computing, Seattle, Wash., 1974, pp. 323-333.]] Google ScholarGoogle Scholar
  17. 17 LEvitt, K.N., AND KarTz, W.H. Cellular arrays for the solution of graph problems. Commun. ACM 15, 9 (Sept. 1972), 789-801.]] Google ScholarGoogle Scholar
  18. 18 NASSIMI, D., AND SAHNI, S. Parallel permutation and sorting networks and a new generalizedconnection network. Preprint, Univ. of Minnesota, Minneapolis, Minn., 1979.]] Google ScholarGoogle Scholar
  19. 19 NASSIMI, D., AND SAHNI, S. Bitonic sort on a mesh-connected parallel computer. IEEE Trans. Comput. C-28 (1979), 2-7.]]Google ScholarGoogle Scholar
  20. 20 OPFERMAN, D.C., AND TSAo-Wu, N.T. On a class of rearrangeable switching networks. Bell Syst. Tech. J. 50 (1971), 1579-1618.]]Google ScholarGoogle Scholar
  21. 21 ORcu~r, S.E. Parallel solution methods for triangular linear systems of equations. Tech. Rep. 77, Digital Systems Laboratory, Stanford Univ., Stanford, Calif., 1974.]] Google ScholarGoogle Scholar
  22. 22 PEASE, M.C. Matrix inversion using parallel processing. J. ACM 14, 4 (Oct. 1967), 757-764.]] Google ScholarGoogle Scholar
  23. 23 PEASS, M.C. An adaptation of the fast Fourier transform for parallel processing. J. ACM 15, 2 (April 1968), 252-264.]] Google ScholarGoogle Scholar
  24. 24 PRF. PARATA, F.P. Parallelism in sorting. Proc. 1977 Int. Conf. on Parallel Processing, Detroit, Mich., 1977, pp. 202-206.]]Google ScholarGoogle Scholar
  25. 25 PREPARATA, F.P., AND SARWATE, D.V. An improved parallel processor bound in fast matrix inversion. Inf. Proc. Letters 7 (1978), 178-150.]]Google ScholarGoogle Scholar
  26. 26 SAMr. H, A., AND BRENT, R. Solving triangular systems on a parallel computer. SIAM J. Numer. Anal. (1977), 1101-1113.]]Google ScholarGoogle Scholar
  27. 27 STONr., H.S. Parallel processing with the perfect shuffle. IEEE Trans. Comput. C-20 (1971), 153-161.]]Google ScholarGoogle Scholar
  28. 28 VALIANT, L.G. Parallelism in comparison problems. SIAM J. Cornput. 4 (1975), 348-355.]]Google ScholarGoogle Scholar
  29. 29 WAKSMAN, A. A permutation network. J. ACM 15, 1 (Jan. 1968), 159-163.]] Google ScholarGoogle Scholar
  30. Several useful surveys of algorithms for parallel numerical and nonnumerical computation have appeared. See Heller (1978), Miranker (1971), Kuck (1975), and Stone (1975b).]]Google ScholarGoogle Scholar
  31. ABRAMSON, N., AND KUO, F.F., EDS. Computer'Communication Networks. Prentice-Hall, Englewood Cliffs, N.J., 1973.]]Google ScholarGoogle Scholar
  32. ADAMS, D.A. A model for parallel computations. In Parallel Processor Systems, Technologies, and Applications, L.C. Hobbs, D.J. Theis, J. Trimble, H. Titus, and I. Highberg, Eds., Spartan Publishers, Washington, D.C., 1970, pp. 311-333.]]Google ScholarGoogle Scholar
  33. AHO, A., AND ULLMAN, J.D. Dynamic memories with rapid random and sequential access. IEEE Trans. Comput. C-23 (1974), 272-276.]]Google ScholarGoogle Scholar
  34. AKERS, S.B. A rectangular logic array. IEEE Trans. Comput. C-21 (1972), 848-857.]]Google ScholarGoogle Scholar
  35. ANI)r. RSON, G.A. 'Interconnecting a distributed processor system for avionics. Proc. IEEE Symp. on Computer Architecture, Gainesville, Fla., 1973, pp. 1-20.]] Google ScholarGoogle Scholar
  36. ANI)~.RSON, G.A., AND JENSEN, E.D. Computer interconnection structures: Taxonomy, characteristics, and examples. Comput. Surv. 7, 4 (Dec. 1975), 197-213.]] Google ScholarGoogle Scholar
  37. ARJOMANDI, E. A study of parallelism in graph theory. Ph.D. Thesis, Dep. of Computer Science, Univ. of Toronto, Toronto, Ontario, Canada, 1977.]] Google ScholarGoogle Scholar
  38. ARJOMANDI, E., AND CORNF. IL, D.G. Parallel computations in graph theory. Proc. 16th Ann. IEEE Syrup. on Foundations of Computer Science, Berkeley, Calif., 1975, pp. 13-18.]]Google ScholarGoogle Scholar
  39. ARNOLD, R.G., AND PAGE, E.W. A hierarchical, restructurable multimicroprocessor architecture. 3rd Ann. Syrup. on Computer Architecture, Clearwater, Fla., 1976, pp. 40-45.]] Google ScholarGoogle Scholar
  40. AVRIEL, M., AND WILDE, D.J. Optimal search for a maximum with sequences of simultaneous function evaluations. Manage. Sci. 12 (1966), 722-731.]]Google ScholarGoogle Scholar
  41. BAER, J.L., AND RUSSELL, E.C. Preparation and evaluation of computer programs for parallel processing systems. In Parallel Processor Systems, Technologies, and Applications, L.C. Hobbs, D.J. Theis, J. Trimble, H. Titus, and I. Highberg, Eds., Spartan Publishers, Washington, D.C., 1970, pp. 375-415.]]Google ScholarGoogle Scholar
  42. BANDYOPADHYAY, $., BASU, S., AND CHOUDHARY, A.K. A cellular permuter array. IEEE Trans. Comput. C-21 (1972), 1116-1119.]]Google ScholarGoogle Scholar
  43. BARNES, G.H., BROWN, R., KATO, M., KUCK, D., SLOTNiCK, D., AND STOKES, R. The ILLIAC IV computer. IEEE Trans. Comput. C-17 (1968), 746-757.]]Google ScholarGoogle Scholar
  44. BASSALYGO, L.A., GRUSHKO, I.I., AND NEYMAN, V.I. Asymptotic estimation of the number of switching points in nonblocking circuits. Telecommun. Radio Eng. 24 (1970), 34-39.]]Google ScholarGoogle Scholar
  45. BASSALYG0, L.A., AND PINSKER, M.S. On the complexity of optimal nonblocking switching networks without rearrangement. Probl. Inf. Transm. 9 (1973), 84-87 (translation).]]Google ScholarGoogle Scholar
  46. BATCHER, K.E. The flip network in STARAN. Proc. 1976 Int. Conf. on Parallel Processing, Detroit, Mich., 1976, pp. 65-71.]]Google ScholarGoogle Scholar
  47. BATCHER, K.E. STARAN series E. Proc. 1977 Int. Conf. on Parallel Processing, Wayne State Univ., Detroit, Mich., 1977, pp. 140-143.]]Google ScholarGoogle Scholar
  48. BENES, V.E. Algebraic and topological properties of connecting networks. Bell Syst. Tech. J. 41 (1962), 1249-1273.]]Google ScholarGoogle Scholar
  49. BENES, V.E. Permutation groups, complexes, and rearrangeable connecting networks. Bell Syst. Tech. J. 43 (1964), 1619-1640.]]Google ScholarGoogle Scholar
  50. BENES, V.E. Optimal rearrangeable multistage connecting networks. Bell Syst. Tech. J. 42 (1964), 1641-1656.]]Google ScholarGoogle Scholar
  51. BENES, V.E. Applications of group theory to connecting networks. Bell Syst. Tech. J. 54 (1975), 4O7-42O.]]Google ScholarGoogle Scholar
  52. BERNSTEIN, A. Analysis of programs for parallel processing. IEEE Trans. Electron. Comput. EC-15 (1966), 757-763.]]Google ScholarGoogle Scholar
  53. BOULTIS, R.L., AND FAISS, R.O. STARAN E performance and LACIE algorithms. Proc. 1977 Int. Conf. on Parallel Processing, Wayne State Univ., Detroit, Mich., 1977, pp. 144-152.]]Google ScholarGoogle Scholar
  54. BREDT, T.H. A survey of models for parallel computing. Tech. Rep. 8, Stanford Univ. Electronics Lab., Palo Alto, Calif., 1970.]] Google ScholarGoogle Scholar
  55. BREDT, T.H., AND MCCLUSKEY, E.J. Analysis and synthesis of control mechanisms for parallel processes. In Parallel Processor Systems, Technologies, and Applications, L.C. Hobbs, D.J. Theis, J. Trimble, H. Titus, and I. Highberg, Eds., Spartan Publishers, Washington, D.C., 1970, pp. 287-296.]]Google ScholarGoogle Scholar
  56. BRENT, R. On the addition of binary numbers. IEEE Trans. Comput. C-19 (1970), 758-759.]]Google ScholarGoogle Scholar
  57. BRENT, R. The parallel evaluation of arithmetic expressions in logarithmic time. In Complexity of Sequential and Parallel Numerical Algorithms, J.F. Traub, Ed., Academic Press, New York, pp. 83- 102.]]Google ScholarGoogle Scholar
  58. BRENT, R. The parallel evaluation of general arithmetic expressions. J. ACM 21, 2 (April 1974), 201-206.]] Google ScholarGoogle Scholar
  59. BRENT, R., KUCK, D., AND MARUYAMA, K. The parallel evaluation of arithmetic expressions without divisions. IEEE Trans. Comput. C-23 (1973), 532-534.]]Google ScholarGoogle Scholar
  60. BRINSFIELD, W.A., AND MILLER, R.E. On the composition of parallel program schemata. Conf. Rec. IEEE 12th Ann. Syrup. on Switching and Automata Theory, East Lansing, Mich., 1971, pp. 20-23.]]Google ScholarGoogle Scholar
  61. BRINSFIELD, W.A., AND MILLER, R.E. Insertion of parallel program schemata. Proc. 7th Ann. Princeton Conf. Information Sciences and Systems, Princeton, N.J., 1973.]]Google ScholarGoogle Scholar
  62. BUDNIK, P., AND KUCK, D.J. The organization and use of parallel memories. IEEE Trans. Comput. C-20 (1971), 1566-1569.]]Google ScholarGoogle Scholar
  63. BUZBEE, B.L. A fast Poisson solver amenable to parallel computation, iEEE Trans. Comput. C-22 (1973), 793-796.]]Google ScholarGoogle Scholar
  64. CALLAHAN, D. Parallel solution of sparse simultaneous linear equations. Tech. Rep., Dep. of Electrical Engineering, Univ. of Michigan, Ann Arbor, Mich., 1973.]]Google ScholarGoogle Scholar
  65. CANTOR, D.G. On nonblocking switching networks. Networks I (1971), 367-377.]]Google ScholarGoogle Scholar
  66. CARROLL, A.B., AND WETHERALD, R.?. Applications of parallel processing to numerical weather prediction. J. ACM 14, 3 (July 1967), 591-614.]] Google ScholarGoogle Scholar
  67. CASTI, J.L., RICHARDSON, M.H., AND LARSON, R.E. Dynamic programming in parallel computers. J. Optim. Theory Appl. 12 (1973), 423-438.]]Google ScholarGoogle Scholar
  68. CHANDRA~ A.K. Independent permutations, as related to a problem of Moser and a theorem of Polya. J. Comb. Theory Series A 16 (1974), 111-120.]]Google ScholarGoogle Scholar
  69. CHAZAN, D., AND MIRANKER, W.L. Chaotic relaxation. Linear Alg. Appl. 2 (1969), 199-222.]]Google ScholarGoogle Scholar
  70. CHAZAN, D., AND MIRANKER, W.L. A nongradient and parallel algorithm for unconstrained minimization. SlAM J. Control 8 (1970), 207-217.]]Google ScholarGoogle Scholar
  71. CHEN, I.N. A cellular data manipulating array. Proc. 1975 Sagamore Conf. on Parallel Processing, Sagamore Lake, N.Y., 1975, p. 114.]]Google ScholarGoogle Scholar
  72. CHEN, S.C. Speedup of iterative programs in multiprocessor systems. Ph.D. Thesis, Computer Science Dep., Univ. of Illinois at Urbana, Urbana, Ill., 1975 {Rep. 694 (NSF-OCA-GJ-36936-000004)}.]] Google ScholarGoogle Scholar
  73. CHEN, S.C. Time and parallel processor bounds for linear recurrence systems with constant coefficients. Proc. 1976 Int. Conf. on Parallel Processing, Detroit, Mich., 1976, pp. 196-205.]]Google ScholarGoogle Scholar
  74. CHEN, S.C., AND KUCK, D.J. Time and parallel processor bounds for linear recurrence systems. IEEE Trans. Comput. C-24 (1975), 701-717.]]Google ScholarGoogle Scholar
  75. CHEN, S.C., AND SAMEH, A. On parallel triangular system solvers. Proc. 1975 Sagamore Conf. on Parallel Processing, Sagamore Lake, N.Y., 1975, pp. 237-238.]]Google ScholarGoogle Scholar
  76. CHEN, T.C. Parallelism, pipelining and computer efficiency. Comput. Design 10 (1971), 69-74.]]Google ScholarGoogle Scholar
  77. CHEN, T.C. Unconventional superspeed computer systems. AFIPS Proc. 1971 Spring JCC, Vol. 38, AFIPS Press, Arlington, Va., pp. 365-371.]]Google ScholarGoogle Scholar
  78. CHrN, Y.K., AND FENG, T. A parallel algorithm for the maximum flow problem (summary). Proc. 1973 Sagamore Conf. on Parallel Processing, Sagamore Lake, N.Y., 1973, p. 60.]]Google ScholarGoogle Scholar
  79. COLE, S.N. Real-time computation by n-dimensional arrays of finite-state machines. IEEE Trans. Comput. C-18 (1969), 349-365.]]Google ScholarGoogle Scholar
  80. COPPAOr., S., AND SCHWARTZ, J.T. A fast switch. Amer. Math. Monthly 83 (1976), 711-717.]]Google ScholarGoogle Scholar
  81. CRANE, B.A., AND GiTHF. NS, J.A. Bulk processing in distributed logic memory. IEEE Trans. Electron. Comput. EC-14 (1965), 186-196.]]Google ScholarGoogle Scholar
  82. CSANKY, L. On the parallel complexity of some computational problems. Ph.D. Dissertation, Dep. of Computer Science, Univ. of California, Berkeley, Calif., 1974.]]Google ScholarGoogle Scholar
  83. CYRE, W.R., AND LIPOVSKI, G.J. On generating multipliers for a cellular fast Fourier transform processor. IEEE Trans. Comput. C-21 (1972), 83-87.]]Google ScholarGoogle Scholar
  84. DAVIDSON, I.A., AND FIELD, J.A. Design criteria for a switch for a multiprocessor computing system. Proc. 1975 Sagamore Conf. on Parallel Processing, Sagamore Lake, N.Y., 1975, pp 110-113.]]Google ScholarGoogle Scholar
  85. DENNIS, J.B., AND MISUNAS, D.P. A computer architecture for highly parallel signal processing. Proc. ACM 1974 National Conf., San Diego, Calif., pp. 402-409.]]Google ScholarGoogle Scholar
  86. DENNIS, J.B., AND MISUNAS, D.P. A preliminary architecture for a basic data-flow processor. Proc. 2nd Ann. IEEE Symp. on Computer Architecture, Houston, Texas, 1975, pp. 126-132.]] Google ScholarGoogle Scholar
  87. DONNELLY, J.D. Periodic chaotic relaxation. Linear Alg. Appl. 4 (1971), 117-128.]]Google ScholarGoogle Scholar
  88. DORN, W.S., Hsu, N.C., AND RIVLIN, T~J. Some mathematical aspects of parallel computation. Tech. Rep. RC-647, IBM Thomas J. Watson Research Center, Yorktown Heights, New York, 1962.]]Google ScholarGoogle Scholar
  89. DowNs, R.S. Real-time algorithms and data management on Illiac IV. IEEE Trans. Comput. C-22 (1973), 773-777.]]Google ScholarGoogle Scholar
  90. DRYSDALE, R.L. Sorting networks which generalize Batcher's odd-even merge. Honors Paper, Knox College, Galesburg, Ill., 1973.]]Google ScholarGoogle Scholar
  91. ECKSTEIN, D. Parallel graph processing using depth-first search and breadth-first search. Ph.D. Thesis, Univ. of Iowa, 1977.]] Google ScholarGoogle Scholar
  92. ENSLOW, P.H., ED. Multiprocessors and parallel processors. John Wiley & Sons, New York, 1974.]]Google ScholarGoogle Scholar
  93. ERMANN, R.N., A~D GROSKY, W.I. Some computation and systems-theoretic properties of regular processor networks. Proc. 1976 Int. Conf. on Parallel Processing, Detroit, Mich., 1976, pp. 230-234.]]Google ScholarGoogle Scholar
  94. ESTRIN, G., BUSSELL, B., TURN, R., AND BIBB, J. Parallel processing in a restructurable computer system. IEEE Trans. Electron. Comput. EC-12 (1963), 747-755.]]Google ScholarGoogle Scholar
  95. EVEN, S. Parallelism in tape sorting. Commun. ACM 17, 4 (April 1974), 202-204.]] Google ScholarGoogle Scholar
  96. EVENSEN, A.J., AND TROY, J.L. Introduction to the architecture of a 288-element PEPE. Proc. 1973 Sagamore Conf. on Parallel Processing, Sagamore Lake, N.Y., 1973, pp. 162-169.]]Google ScholarGoogle Scholar
  97. FALKOFF, A.D. Algorithms for parallel search memories. J. ACM 9, 4 (Oct. 1962), 488-511.]] Google ScholarGoogle Scholar
  98. FENG, T.Y. Data manipulating functions in parallel processors and their implementations, iEEE Trans. Comput. C-23 (1964), 309-318.]]Google ScholarGoogle Scholar
  99. FENC, T.Y. A configurable multi-microprocessor organization. In Micro-Architecture of Computer Systems, Proc. Euromicro, Nice Workshop, 1975, R. Hartenstein, Ed., N(irth-Holland, Amsterdam, pp. 207-219.]]Google ScholarGoogle Scholar
  100. FISHER, D. Program analysis for multi-processing. Tech. Rep. TR-67-2, Burroughs Corp., 1967. FLOYD, R.W., AND KNUTH, D.E. The Bose-Nelson sorting problem. CS Rep. 70-177, Stanford Univ., Stanford, Calif., 1976.]]Google ScholarGoogle Scholar
  101. FLYNN, M.J. Very-high-speed computing systems. Proc. IEEE 54 (1966), 1901-1909.]]Google ScholarGoogle Scholar
  102. FLYNN, M.J., PoovIN, A., AND SHIMIZU, K. A multiple instruction stream processor with shared resources. In Parallel Processor Systems, Technologies, and Applications, L.C. Hobbs, D.J. Theis, J. Trimble, H. Titus, and I. Highberg, Eds., Spartan Publishers, Washington, D.C., 1970, pp. 215-286.]]Google ScholarGoogle Scholar
  103. GALE, D., AND KARP, R.K. A phenomenon in the theory of sorting. IEEE Conf. Rec. of llth Ann. Symp. on Switching and Automata Theory, Santa Monica, Calif., 1970, pp. 51-59.]]Google ScholarGoogle Scholar
  104. GAVRIL, F. Merging with parallel processors. Commun. ACM 18, 10 (Oct. 1975), 588-591.]] Google ScholarGoogle Scholar
  105. GENTLEMAN, W.M. Some complexity results for matrix computations on parallel processors. Tech. Rep., Dep. of Computer Science, Univ. of Waterloo, Waterloo, Ontario, Canada, 1976.]]Google ScholarGoogle Scholar
  106. GEORGE, A., POOLE, W.G., AND VOIOHT, R.G. Analysis of dissection algorithms for vector computers. Tech. Rep., Institute for Computer Applications in Science and Engineering, Hampton, Va., 1976.]]Google ScholarGoogle Scholar
  107. GILL, S. Parallel programming. Comput. J. I (1958), 2-10.]]Google ScholarGoogle Scholar
  108. GILMORE, P.A. Structuring of parallel algorithms, j. ACM 15, 2 (April 1968), 176-192.]] Google ScholarGoogle Scholar
  109. GILMORE, P.A. Parallel relaxation. Tech. Rep., Goodyear Aerospace Corp., Akron, Ohio, 1971.]]Google ScholarGoogle Scholar
  110. GOKE, R. Connecting networks for partitioning polymorphic systems. Ph.D. Dissertation, Dep. of Electrical Engineering, Univ. of Florida, Gainesville, Fla., 1976.]]Google ScholarGoogle Scholar
  111. GOKE, R., AND LIPOVSKI, G.J. Banyan networks for partitioning on multiprocessor systems. Proc. 1st Ann. Symp. on Computer Architecture, Gainesville, Fla., 1973, pp. 21-30.]] Google ScholarGoogle Scholar
  112. GOLOMB, S.W. Permutations by cutting and shuffling. SIAM Rev. 3 (1961), 293-297.]]Google ScholarGoogle Scholar
  113. GONZALES, M.J., AND RAMAMOORTHY, C.V. Recognition and representation of parallel processable streams in computer programs. In Parallel Processor Systems, Technologies and Applications, L.C.]]Google ScholarGoogle Scholar
  114. Hobbs, D.J. Theis, J. Trimble, H. Titus, and I. Highberg, Eds., Spartan Publishers, Washington, D.C., 1970, pp. 335-373.]]Google ScholarGoogle Scholar
  115. GONZALES, M.J., AND RAMAMOORTHY, C.V. Program suitability for parallel processing. IEEE Trans. Comput. C-20 (1971), 647-654.]]Google ScholarGoogle Scholar
  116. GREEN, M.W. Some improvements in nonadaptive sorting algorithms. Proc. 6th Ann. Princeton Conf.' on Information Sciences and Systems, Princeton, N.J., 1972, pp. 387-391.]]Google ScholarGoogle Scholar
  117. HARADH, K. Sequential permutation networks. IEEE Trans. Comput. C-21 (1972), 472-479.]]Google ScholarGoogle Scholar
  118. HELLER, D. A determinant theorem with applications to parallel algorithms. Tech. Rep., Dep. of Computer Science, Carnegie-Mellon Univ., Pittsburgh, Pa., 1973.]]Google ScholarGoogle Scholar
  119. HELLER, D. A survey of parallel algorithms in numerical linear algebra. SIAM Rev. 20 (1978), 740- 777. See also Tech. Rep., Dep. of Computer Science, Carnegie-Mellon Univ., Pittsburgh, Pa., 1976.]]Google ScholarGoogle Scholar
  120. HOLLAND, J. A universal computer capable of executing an arbitrary number of subprograms simultaneously. Proc. IEEE Eastern Joint Computer Conference, Boston, Mass., pp. 108-113.]]Google ScholarGoogle Scholar
  121. HYAFIL, L., AND KUNC, H.T. Parallel algorithms for solving triangular linear systems. Tech. Rep., Dep. of Computer Science, Carnegie-Mellon Univ., Pittsburgh, Pa., 1974.]]Google ScholarGoogle Scholar
  122. HYAFIL, L., AND KUNG, H.T. The complexity of parallel evaluation of linear recurrences. Proc. 7th Ann. ACM Symp. on Theory of Computing, Albuquerque, N.M., 1975, pp. 12-22.]] Google ScholarGoogle Scholar
  123. HYAFIL, L., AND KUNG, H.T. Bounds on the speed-ups of parallel evaluation of recurrences. Proc. 2nd USA-Japan Computer Conf., Tokyo, 1975, pp. 178-182.]]Google ScholarGoogle Scholar
  124. HYAFIL, L., AND KUNG, H.T. The complexity of parallel evaluation of linear recurrences. J. ACM 24, 3 (July 1977), 513-521.]] Google ScholarGoogle Scholar
  125. JOEL, A.E. On permutation switching networks. Bell Syst. Tech. J. 47 (1968), 813-822.]]Google ScholarGoogle Scholar
  126. KARP, R.M., AND MIRANKER, W. Parallel minimax search for a maximum. J. Comb. Theory 4 (1968), 19-35.]]Google ScholarGoogle Scholar
  127. KAge, R.M., AND MILLER, R.E. Parallel program schemata. J. Comput. Sys. Sci. 3 (1969), 147-195.]]Google ScholarGoogle Scholar
  128. KARP, R.M., MILLER, R.E., AND WINOORAD, S. The organization of computations for uniform recurrence equations. J. ACM 14, 3 (July 1967), 563-590.]] Google ScholarGoogle Scholar
  129. KAUTZ, W.H. Cellular logic-in-memory arrays. IEEE Trans. Comput. C-18 (1969), 719-727.]]Google ScholarGoogle Scholar
  130. KAUTZ, W.H. The design of optimum interconnection networks for multiprocessors. In Structure et Conception des Ordinateurs (Architecture and Design of Digital Computers), Guy Boulaye, Ed., Dunod Publishers, Paris, 1971, pp. 249-278.]]Google ScholarGoogle Scholar
  131. KAUTZ, W.H., LEvn~r, K.N., AND WAKSMAN, A. Cellular interconnection arrays. IEEE Trans. Comput. C-17 (1968), pp. 443-451.]]Google ScholarGoogle Scholar
  132. KAUTZ, W.H., PEASE, M.C., AND GREEN, M.W. Cellular logic-in-memory arrays. Final Rep. Pt. 1, Project 5509, NONR-4833 (00), Stanford Research Institute, Paid Alto, Calif., 1970.]]Google ScholarGoogle Scholar
  133. KELLER, R.M. On maximally parallel schemata. Conf. Rec. llth Ann. IEEE Syrup. on Switching and Automata Theory, Santa Monica, Calif., 1970, pp. 32-50.]]Google ScholarGoogle Scholar
  134. KELLER, R.M. On the decomposition of asynchronous systems. Conf. Rec. 13th Ann. IEEE Symp. on Switching and Automata Theory, Baltimore, Md., 1972, pp. 78-89.]]Google ScholarGoogle Scholar
  135. KNIGHT, J.C., POOLE, W.G., JR., AND VOICT, R.G. System balance analysis for vector computers. Proc. ACM Ann. Conf., Minneapolis, Minn., 1975, pp. 163-168.]] Google ScholarGoogle Scholar
  136. KOGGE, P.M. Parallel algorithms for the solution of recurrence problems. Tech. Rep., Digital Systems Laboratory, Stanford Univ., Stanford, Calif., 1972.]]Google ScholarGoogle Scholar
  137. KOCGE, P.M. The numerical stability of parallel algorithms for solving recurrence problems. Tech. Rep., Digital Systems Laboratory, Stanford Univ., Stanford, Calif., 1972.]]Google ScholarGoogle Scholar
  138. KOCGE, P.M. Parallel solution of recurrence problems. IBM J. Res. Devel. 18 (1974), 183-184.]]Google ScholarGoogle Scholar
  139. KOCGE, P.M., AND STONE, H.S. A parallel algorithm for the efficient solution of a general class of recurrence equations. IEEE Trans. Comput. C-22 (1973), 786-792.]]Google ScholarGoogle Scholar
  140. KOTOV, V.E. Towards automatic construction of parallel programs. Proc. Symp. on Theoretical Programming, Novosibirsk, USSR, 1972, pp. 309-332.]] Google ScholarGoogle Scholar
  141. KoTov, V.E., AND NARINYANI, A.S. On transformation of sequential programs into asynchronous parallel programs. Proc. 1968 IFIP Congress, Edinburgh, pp. 351-357.]]Google ScholarGoogle Scholar
  142. KUCK, D.J. Multioperation machine computational complexity. Proc. of Symp. on Complexity of Sequential and Parallel Numerical Algorithms, J.F. Traub, Ed., Academic Press, New York, pp. 17- 48.]]Google ScholarGoogle Scholar
  143. KUCK, D.J. Parallel processing architecture, a s?vey. Proc. 1975 Sagamore Conf. on Parallel Processing, Sagamore Lake, N.Y., 1975, pp. 15-39.]]Google ScholarGoogle Scholar
  144. KUCK, D.J., I~URIE, D.H., AND MURAOKA, Y. Interconnection networks for processors and memories in large systems. COMPCON 72, San Francisco, Calif., 1972, pp. 131-134.]]Google ScholarGoogle Scholar
  145. KUCK, D.J., AND MARUYAMA, K.M. The parallel evaluation of arithmetic expressions of special forms. Rep. RC4726, IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y., 1973.]]Google ScholarGoogle Scholar
  146. KUCK, D.J., AND MARUYAMA, K.M. Time bounds on the parallel evaluation of arithmetic expressions. SIAM J. Comput. 4 (1974), 147-162.]]Google ScholarGoogle Scholar
  147. KUCK, D.J., AND SAMEH, A.H. Parallel computation of eigenvalues of real matrices. Proc. 1971 IFIP Congress, Vol. II, North-Holland, Amsterdam-London, pp. 1266-1272.]]Google ScholarGoogle Scholar
  148. KUKREJA, N., AND CHEN, I.N. Combinatorial and sequential cellular structures, iEEE Trans. Comput. C-22 (1973), 813-823.]]Google ScholarGoogle Scholar
  149. KUNC, H.T. Synchronous and asynchronous parallel algorithms for multiprocessors. In Algorithms and Complexity, J.F. Traub, Ed., 1967, pp. 153-200.]]Google ScholarGoogle Scholar
  150. LADNER, R.E., AND FISHER, M.J. Parallel prefix computations. Proc. 1977 Int. Conf. on Parallel Processing, Detroit, Mich., 1977, pp. 218-223.]]Google ScholarGoogle Scholar
  151. LAMBIOTTE, J.J., JR., AND VOIGT, R.G. The solution of tridiagonal linear systems on the CDC STAR-100 computer. ACM Trans. Math. Softw. 1, 4 (Dec. 1975), 308-329.]] Google ScholarGoogle Scholar
  152. LAMPORT, L. The parallel execution of DO loops. Commun. ACM, 17, 2 (Feb. 1974), 83-93.]] Google ScholarGoogle Scholar
  153. LANG, T. Interconnections between memory modules using the shuffle-exchange network. IEEE Trans. Comput. C-25 (1976), 496-503. See also Tech. Rep. 76, Digital Systems Laboratory, Stanford Univ., Stanford, Calif., 1973.]]Google ScholarGoogle Scholar
  154. LANG, T., AND STONE, H.S. A shuffle-exchange network with simplified control. IEEE Trans. Comput. C-25 (1976), 55-65.]]Google ScholarGoogle Scholar
  155. LANGE, R.G. High level language for associative and parallel computation with STARAN. Proc. 1976 Int. Conf. on Parallel Processing, Detroit, Mich., 1976, pp. 170-176.]]Google ScholarGoogle Scholar
  156. LARSON, R.E., RICHARDSON, M.H., AND BREE, D.W. Dynamic programming in parallel computers. 4th Ann. Hawaii Conf. on Systems Science, pp. 256-269.]]Google ScholarGoogle Scholar
  157. LARSON, R.E., RICHARDSON, M.H., AND CASTI, J.L. Dynamic programming with parallel computers for use in Air Force applications. Final Rep., AFOSR Project F44620-70-C0084, SCI Project U956, System Control, Inc., Palo Alto, Calif., 1971.]]Google ScholarGoogle Scholar
  158. LARSON, R.E., AND TSE, E. Modal trajectory estimation and parallel computers. 2nd Syrup. on Nonlinear Estimation Theory, San Diego, Calif., 1971, pp. 188-198.]]Google ScholarGoogle Scholar
  159. LARSON, R.E., AND TSE, E. Parallel computation of the modal trajectory estimate. Joint Automata Control Conf., Stanford, Calif. See also 5th Ann. Hawaii Conf. on System Sciences, Honolulu, 1972, pp. 495-499.]]Google ScholarGoogle Scholar
  160. LARSON, R.E., AND TSE, E. Parallel processing algorithms for the optimal control of nonlinear dynamic systems. IEEE Trans. Comput. C-22 (1973), 777-785.]]Google ScholarGoogle Scholar
  161. LAWRIE, D.H. Memory-processor communication networks. Tech. Rep. and Thesis, UIU CSCS-R- 75-557, Computer Science Dep., University of Ill., Urbana, Ill., 1973.]] Google ScholarGoogle Scholar
  162. LAWRiE, D.H. Access and alignment of data in an array processor. IEEE Trans. Comput. C-24 (1975), 1145-1155.]]Google ScholarGoogle Scholar
  163. LAWRIE, D.H., LAYMAN, T., BAER, D., AND RANDAL, J.M. GLYPNIR--A programming language for Illiac iV. Commun. ACM 18, 3 (March 1975), 157-164.]] Google ScholarGoogle Scholar
  164. LEE, C.C., AND FENC;, T. Sorting algorithms for parallel processing (summary). Proc. 1975 Sagamore Conf. on Parallel Processing, Sagamore Lake, N.Y., 1975, p. 239.]]Google ScholarGoogle Scholar
  165. LEHMAN, M. A survey of problems and prehminary results concerning parallel processing and parallel processors. Proc. IEEE 54 (1966), 1889-1901.]]Google ScholarGoogle Scholar
  166. LEONDES, C., AND RUBINOFF, M. DINA, a digital analyzer for Laplace, Poisson, diffusion and wave equations. AIEE Trans. ( Commun. & Electron.) 71 (1952), 303-309.]]Google ScholarGoogle Scholar
  167. LEVITT, K.N., GREEN, M.W., AND GOLDBERG, J. A study of the data communication problems in a self-repairable multiprocessor. Proc. 1968 Spring JCC, AFIPS Press, Arlington, Va., pp. 515-527.]]Google ScholarGoogle Scholar
  168. LIPOVSKI, G.J. The architecture of a large associative processor. Proc. 1970 Spring JCC, Vol. 37, AFIPS Press, Arlington, Va., pp. 385-395.]]Google ScholarGoogle Scholar
  169. LIPOVSKI, G.J. On a varistructured array of microprocessors. IEEE Trans. Comput. C-26 (1977), 125-138.]]Google ScholarGoogle Scholar
  170. LIPOVSKI, G.J., AND TRIPATHI, i. A reconfigurable varistructure array processor. Proc. 1977 Int. Conf. on Parallel Processing, Detroit, Mich., 1977, pp. 165-173.]]Google ScholarGoogle Scholar
  171. LIU, C.L. Construction of sorting plans. In Theory of Machines and Computation, Z. Kohavi and A. Paz, Eds., Academic Press, New York, 1971, pp. 87-98.]]Google ScholarGoogle Scholar
  172. LIU, J.W.H. The solution of mesh equations on a parallel computer. Tech. Rep., Dep. of Computer Science, Waterloo Univ., Waterloo, Ontario, Canada, 1974.]]Google ScholarGoogle Scholar
  173. MADSEN, N.K., RODRIGUE, G.N., AND KARUSH, J.I. Matrix multiplication by diagonals on a vector/ parallel processor. Inf. Proc. Letters 5 (1976), 41-45.]]Google ScholarGoogle Scholar
  174. MARCUS, M.J. New approaches to the analysis of connecting and sorting networks. Tech. Rep. 486, Research Laboratory of Electronics, M.I.T., Cambridge, Mass., 1972.]]Google ScholarGoogle Scholar
  175. MARUYAMA, K. On the parallel evaluation of polynomials. IEEE Trans. Comput. C.22 (1973), 2-5.]]Google ScholarGoogle Scholar
  176. MARUYAMA, K. The parallel evaluation of matrix expressions. Tech. Rep., IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y., 1973.]]Google ScholarGoogle Scholar
  177. MILLER, J.C.P., AND BROWN, D.J.S. An algorithm for evaluation of remote terms in a linear recurrence relation. Comput. J. 9 (1967), 188-190.]]Google ScholarGoogle Scholar
  178. MILLER, R.E. A comparison of some theoretical models of parallel computation. IEEE Trans. Comput. C-22 (1973), 710-717.]]Google ScholarGoogle Scholar
  179. MIRANKER, W. Parallel methods for evaluating the root of a function. IBM J. Res. Devel. 13 (1967), 297-301.]]Google ScholarGoogle Scholar
  180. MIRANKER, W. A survey of parallelism in numerical analysis. SIAM Rev. 13 (1971), 524-547.]]Google ScholarGoogle Scholar
  181. MIRANKER, W., AND LINIGER, W.M. Parallel methods for the numerical integration of ordinary differential equations. Math. Comp. 21 (1967), 303-320.]]Google ScholarGoogle Scholar
  182. MISUNAS, D.P. A computer architecture for data-flow computation. Master's Thesis, Dep. Electrical Engineering and Computer Science, M.I.T., Cambridge, Mass., 1975.]]Google ScholarGoogle Scholar
  183. MULLER, D.E., AND PREPARATA, F.P. Bounds to complexities of networks for sorting and for switching. J. ACM 22, 2 (April 1975), 195-201.]] Google ScholarGoogle Scholar
  184. MUNRO, I., AND PATTERSON, M. Optimal algorithms for parallel polynomial evaluation. J. Comput. Sys. Sci. 7 (1973), 189-198. See also Conf. Rec. 12th Ann. Syrup. on Switching and Automata Theory, East Lansing, Mich., 1971.]]Google ScholarGoogle Scholar
  185. MURAOKA, Y. Parallelism exposure and exploitation in programs. Ph.D. Thesis, Computer Science Dep., Univ. of Illinois, Urbana, Ill., 1971 (Tech. Rep. 424).]] Google ScholarGoogle Scholar
  186. MURAOKA, Y., AND KUCK, D.J. On the time required for a sequence of matrix products. Commun. ACM 16, 1 (Jan. 1973), 22-26.]] Google ScholarGoogle Scholar
  187. MURTHA, J.C. Highly parallel information processing systems. Adv. Comput. 7 (1966), 2-116.]]Google ScholarGoogle Scholar
  188. NARINYANI, A.S. Looking for a theory of parallel computation models. Proc. Symp. Theoretical Programming, Novosibirsk, USSR, 1972, pp. 247-284.]] Google ScholarGoogle Scholar
  189. NEIMAN, V.I. Structure et commandes optimales des reseaux de connections sans blockage. Ann. Telecommun. 24 (1969), 232-238.]]Google ScholarGoogle Scholar
  190. NIEVERGELT, J. Parallel methods for integrating ordinary differential equations. Commun. ACM 7, 12 (Dec. 1964), 731-733.]] Google ScholarGoogle Scholar
  191. OKADA, Y., TAJIMA, M., ANO MORI, R. A novel multiprocessor array. 2nd Symp. on Microarchitecture (Euromicro), North-Holland, Amsterdam, 1976.]]Google ScholarGoogle Scholar
  192. ORcu~r, S.E. Computer organization and algorithms for very high-speed computation. Ph.D. Thesis, Stanford Univ., Stanford, Calif., 1974.]]Google ScholarGoogle Scholar
  193. PEASE, M.C. The implicit binary n-cube microprocessor array. IEEE Trans. Comput. Co26 (1975), 153-161.]]Google ScholarGoogle Scholar
  194. PIPP~NGER, N. The complexity theory of switching networks. Tech. Rep., Research Laboratory of Electronics, M.I.T., Cambridge, Mass., 1973.]]Google ScholarGoogle Scholar
  195. PIPPENaER, N. On the complexity of strictly nonblocking concentration networks. IEEE Trans. Commun. COM-22 (1974), 1890-1893.]]Google ScholarGoogle Scholar
  196. PIPPENGER, N. On crossbar switching networks. IEEE Trans. Commun. COM-23 (1975), 646-659.]]Google ScholarGoogle Scholar
  197. PmTLE, M. Intercommunication of processors and memory. Proc. Fall JCC, Vol. 31, Thompson Publishing, Washington, D.C., pp. 621-633.]]Google ScholarGoogle Scholar
  198. PREPARATA, F.P. New parallel-sorting schemes. IEEE Trans. Comput. C-27 (1978), 669-673.]]Google ScholarGoogle Scholar
  199. Rr.~TER, R. Scheduling parallel computations. J. ACM 15, 4 (Oct. 1968), 590-599.]] Google ScholarGoogle Scholar
  200. RoDmoUr. Z, J.E. A graph model for parallel computation. Ph.D. Dissertation, M.I.T., Cambridge, Mass., 1967. See also Project MAC Rep. ESL-R-398, MAC-TR-64, Sept. 1969.]] Google ScholarGoogle Scholar
  201. RODRiGUEZ, J.E. Parallel processes, schemata, and transformations. IBM Res. Rep. RC 2912, IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y., 1970.]]Google ScholarGoogle Scholar
  202. ROSEN, K.F. An algorithm for random walks on highly parallel machines. Tech. Rep. TR-15, Cooley Electronics Laboratory, Univ. of Michigan, Ann Arbor, Mich., 1964.]]Google ScholarGoogle Scholar
  203. ROSENFELD, J.L. A case study in programming for parallel processors. Commun. ACM 12, 12 (Dec. 1969), 645-655.]] Google ScholarGoogle Scholar
  204. ROSENFELO, J.L., AND DRiSCOLL, C.G. Solution of the Dirichlet problem on a simulated parallel processing system. Proc. IFIP Congress 1968, North-Holland, Amsterdam, 1969, pp. 499-507.]]Google ScholarGoogle Scholar
  205. SAMEH, A.H. On Jacobi and Jacobi-like algorithms for a parallel computer. Math. Comp. 25 (1971), 579-590.]]Google ScholarGoogle Scholar
  206. SAMEH, A.H. Linear system solvers for parallel computers. Tech. Rep., Dep. of Computer Science, Univ. of Illinois, Urbana, Ill., 1975.]]Google ScholarGoogle Scholar
  207. SAMEH, A., AND KUCK, D. Linear system solvers for parallel computers. Rep. 701 (NSF-OCS-GJ- 36936-000009), Computer Science Dep., Univ. of Illinois, Urbana, Ill., 1975.]]Google ScholarGoogle Scholar
  208. SAMEH, A., AND KUCK, D. A parallel QR-algorithm for symmetric tridiagonal matrices. IEEE Trans. Comput. C-26 (1977), 147-153.]]Google ScholarGoogle Scholar
  209. SAMEH, A., ANO KUCK, D. On stable parallel linear system solvers. J. ACM 25, 1 (Jan. 1978), 81-91.]] Google ScholarGoogle Scholar
  210. SAVAGr., C. Parallel algorithms for graph-theoretic problems. Ph.D. Dissertation, Univ. of illinois, Urbana, Ill., 1978.]]Google ScholarGoogle Scholar
  211. SCHWARTZ, J. Large parallel computers. J. ACM 13, 1 (Jan. 1966), 25-32.]] Google ScholarGoogle Scholar
  212. S~^NNON, C.E. Memory requirements in a telephone exchange. Bell Syst. Tech. J. 29 (1950), 347- 349.]]Google ScholarGoogle Scholar
  213. SHAPmo, H.D. Storage schemes in parallel memories. Proc. I975 Sagamore Conf. On Parallel Processing, Sagamore Lake, N.Y., 1975, pp. 159-164.]]Google ScholarGoogle Scholar
  214. SHArmo, H.D. Theoretical limitations on the use of parallel memories. Ph.D. Thesis, Computer Science Dep., Univ. of Illinois, Urbana, ill., 1976.]]Google ScholarGoogle Scholar
  215. SHr~OLER, G.S. Parallel numerical methods for the solution of equations. Comrnun. ACM 10, 5 (May 1967), 286-291.]] Google ScholarGoogle Scholar
  216. SHEVLER, G.S., AND LEHMAN, M. Evaluation of redundancy in a parallel algorithm. IBM Syst. J. 6 (1967), 142-149.]]Google ScholarGoogle Scholar
  217. S~F. GEL, H.J. Single instruction stream--multiple data stream machine interconnection network design. Proc. 1976 Int. Conf. on Parallel Processing, Detroit, Mich., 1976, pp. 272-280.]]Google ScholarGoogle Scholar
  218. SISCEL, H.J. Analysis techniques for SIMD machine interconnection networks and the effects of processor address masks. IEEE Trans. Cornput. C-26 (1977), 153-161. See also Proc. 1975 Sagamore Conf. on Parallel Computing, Sagamore Lake, N.Y., 1975, pp. 106-109.]]Google ScholarGoogle Scholar
  219. SIEGEL, H.J. The universality of various types of SIMD machine interconnection networks. Proc. IEEE 4th Ann. Symp. on Computer Architecture, Silver Springs, Md., 1977, pp. 70-79.]] Google ScholarGoogle Scholar
  220. SISGEL, H.J., AND SMITH, S.D. Study of multistage SIMD interconnection networks. Proc. IEEE 15th Ann. Symp. on Computer Architecture, Stanford, Calif., pp. 223-229.]] Google ScholarGoogle Scholar
  221. SMITH, B.J. An analysis of sorting networks. Final Tech. Rep., ONR Contract N00014-70-A-0362- OO06, 1972.]] Google ScholarGoogle Scholar
  222. STONE, H.S. The organization of high-speed memory for parallel block transfer of data. IEEE Trans. Comput. C-19 (1970), 47-53.]]Google ScholarGoogle Scholar
  223. STONE, H.S. A logic-in-memory computer. IEEE Trans. Comput. C-18 (1970), 719-727.]]Google ScholarGoogle Scholar
  224. STONE, H.S. Dynamic memories with enhanced data access. IEEE Trans. Comput. C-21 (1972), 359-366.]]Google ScholarGoogle Scholar
  225. STONE, H.S. Problems of parallel computation. In Complexity of Sequential and Parallel Numerical Algorithms, J.F. Traub, Ed., Academic Press, New York, 1973, pp. 1-17.]]Google ScholarGoogle Scholar
  226. STONE, H.S. An efficient parallel algorithm for the solution of a tridiagonal linear system of equations. J. ACM 20, 1 (Jan. 1973), 27-38. ..]] Google ScholarGoogle Scholar
  227. STONE, H.S. Discrete Mathematical Structures and Their Applications. Science Research Associates, Chicago, II1., 1973.]]Google ScholarGoogle Scholar
  228. STONE, H.S. Parallel tridiagonal equation solvers. ACM Trans. Math. Softw. 1, 4 (Dec. 1975a), 289- 307.]] Google ScholarGoogle Scholar
  229. STONE, H.S. Parallel computers. In introduction to Computer Architecture, Science Research Associates, Palo Alto, Calif., 1975b, pp. 318-374.]]Google ScholarGoogle Scholar
  230. SULLIVAN, H., AND BASHKOW, T.R. A large scale, homogeneous, fully distributed parallel machine. Proc. 4th Annual Syrup. on Computer Architecture, Silver Springs, Md., 1977, pp. 105-117.]] Google ScholarGoogle Scholar
  231. SULLIVAN, H., BASHKOW, T.R., AND KLAPPHOLZ, D. High level language constructions in a selforganizing parallel processor. Proc. 1977 Int. Conf. on Parallel Processing, Detroit, Mich., 1977, pp. 163-174.]]Google ScholarGoogle Scholar
  232. SULLIVAN, H., BASHKOW, T.R., AND KLAPPHOLZ, D. A large scale, homogeneous fully distributed parallel machine, II. Proc. 4th Ann. Syrup. on Computer Architecture, Silver Springs, Md., 1977, pp. 118-127.]] Google ScholarGoogle Scholar
  233. SULLIVAN, H., BASHKOW, T.R., KLAPPHOLZ, D., AND COHN, L. The node kernel: resource management in a self organizing parallel processor. Proc. 1977 Int. Conf. on Parallel Processing, Detroit, Mich., 1977, pp. 157-162.]]Google ScholarGoogle Scholar
  234. SWANSON, R.C. Interconnection for parallel memories to unscramble p-ordered vectors. IEEE Trans. Comput. C-23 (1974), 1105-1115.]]Google ScholarGoogle Scholar
  235. THOMPSON, C.D. Generalized connection networks for parallel processor interconnection. IEEE Trans. Comput. C-27 (1978), 1119-1125.]]Google ScholarGoogle Scholar
  236. THOMPSON, C.D., AND KUNG, K.T. Sorting on a mesh-connected parallel computer. Proc. 8th Ann. ACM Syrup. on Theory of Computing, Hershey, Pa., 1976, pp. 59-64.]] Google ScholarGoogle Scholar
  237. THURBER, K.J. Programmable indexing networks. Proc. 1970 Spring JCC, AFIPS Press, Arlington, Va., pp. 51-58.]]Google ScholarGoogle Scholar
  238. THURSER, K.J. Permutation switching networks. Proc. 1971 Computer Designer's Conf., Anaheim, Calif., 1971, pp. 7-24.]]Google ScholarGoogle Scholar
  239. THURBER, K.J. Interconnection networks--A survey and assessment. AFIPS Conf. Proc., Vol. 43, AFIPS Press, Arlington, Va., pp. 909-919.]]Google ScholarGoogle Scholar
  240. TRAUB, J.F. Iterative solution of tridiagonal system's on parallel and vector computers. In Complexity of Sequential and Parallel Numerical Algorithms, Academic Press, New York, 1973, pp. 49-82.]]Google ScholarGoogle Scholar
  241. TROUT, H.R.G. Parallel techniques. Tech. Rep., Dep. of Computer Science, Univ. of Illinois, Urbana, ill., 1972.]]Google ScholarGoogle Scholar
  242. TSAO-Wu, N.T., AND OPrERMAN, D.C. On permutation algorithms for rearrangeable switching networks. Conf. Rec. 1969 IEEE Int. Conf. on Communications, Boulder, Colo., 1969, pp. 10-29-10-34.]]Google ScholarGoogle Scholar
  243. TsE, E. Parallel computation of the conditional mean state estimate for nonlinear systems. 2nd Symp. on Nonlinear Estimation Theory, San Diego, Calif., 1971, pp. 385-395.]]Google ScholarGoogle Scholar
  244. TsE, E., AND LARSON, R.E. Optimum quantization and parallel algorithms for nonlinear state estimation. 3rd Syrup. on Nonlinear Estimation Theory, San Diego, Calif., 1972.]]Google ScholarGoogle Scholar
  245. TUTTLS, P.G. Implementation of selected eigenvalue algorithms on a vector computer. Master's Thesis, Univ. of Virginia, Charlottesville, Va., 1975.]]Google ScholarGoogle Scholar
  246. VALIANT, L.G. The intrinsic complexity of parallelism in comparison problems. Tech. Rep., Dep. of Computer Science, Carnegie-Mellon Univ., Pittsburgh, Pa., 1974.]]Google ScholarGoogle Scholar
  247. VAN VOORHIS, D.C. A lower bound for sorting networks that use the divide-sort-merge strategy. Tech. Rep. 17, Digital Systems Laboratory, Stanford Univ., Stanford, Calif., 1971.]] Google ScholarGoogle Scholar
  248. VAN VOORHIS, D.C. A generalization of the divide-sort-merge strategy for sorting networks. Tech. Rep. 16, Digital Systems Laboratory, Stanford Univ., Stanford, Calif., 1971.]] Google ScholarGoogle Scholar
  249. VAN VOORHXS, D.C. Large {g, d} sorting networks. Tech. Rep. 18, Digital Systems Laboratory, Stanford Univ., Stanford, Calif., 1971.]] Google ScholarGoogle Scholar
  250. VAN VOORaIS, D.C. Toward a lower bound for sorting networks. In Complexity of Computer Computations, Plenum Publishing, New York, 1972, pp. 119-129.]]Google ScholarGoogle Scholar
  251. VAN Voogms, D.C. An economical construction for sorting networks. Working Paper 16/A45 No. 1, IBM Systems Development Division, Los Gatos, Calif. See also Proc. 1974 NCC, AFIPS Press, Arlington, Va., pp. 921-926.]]Google ScholarGoogle Scholar
  252. WAKSMAN, A. On permutation networks. Proc. Hawaii Int. Conf. on System Sciences, Univ. of Hawaii, Honolulu, 1968, pp. 581-582.]]Google ScholarGoogle Scholar
  253. WAaD, R.C. The QR algorithm and Hyman's method on vector computers. Math. Comput. 30 (1976), 132-142.]]Google ScholarGoogle Scholar
  254. WEN, K.Y. Interprocessor connection--Capabilities, exploitation and effectiveness. Ph.D. Thesis, 1976.]] Google ScholarGoogle Scholar
  255. WINOCRAD, S. On the time required to perform addition. J. ACM 12, 2 (April 1965), 277-285.]] Google ScholarGoogle Scholar
  256. WINOGRAD, S. On the time required to perform multiplication. J. ACM 14, 4 (Oct. 1967), 793-802.]] Google ScholarGoogle Scholar
  257. WlTTm, L.D. Efficient message routing in mega-microcomputer networks. Proc. iEEE 3rd Ann. Symp. on Computer Architecture, Clearwater, Fla., 1976, pp. 136-140.]] Google ScholarGoogle Scholar
  258. WoNt, C.K., AND YUE, P.C. Anticipatory control on a permutable memory. IEEE Trans. Comput. C-22 (1973), 481-488.]]Google ScholarGoogle Scholar
  259. WULF, W., AND B~.LL, C.G. C.mmpmA multi-mini-processor. Proc. AFIPS 1972 Fall JCC, Vol. 41, AFIPS Press, Arlington, Va., pp. 765-778.]]Google ScholarGoogle Scholar

Index Terms

  1. Ultracomputers

      Recommendations

      Comments

      Login options

      Check if you have access through your login credentials or your institution to get full access on this article.

      Sign in

      Full Access

      • Published in

        cover image ACM Transactions on Programming Languages and Systems
        ACM Transactions on Programming Languages and Systems  Volume 2, Issue 4
        Oct. 1980
        131 pages
        ISSN:0164-0925
        EISSN:1558-4593
        DOI:10.1145/357114
        Issue’s Table of Contents

        Copyright © 1980 ACM

        Publisher

        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 1 October 1980
        Published in toplas Volume 2, Issue 4

        Permissions

        Request permissions about this article.

        Request Permissions

        Check for updates

        Qualifiers

        • article

      PDF Format

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader