Abstract
Kung [1979b] has recently enunciated a set of principles for designing algorithms for implementation in Very Large Scale Integrated circuitry (VLSI), and supported these principles by displaying a number of particular algorithms based on various "communication geometries". In this paper we will examine a communication geometry which Kung calls the "one-dimensional array of processors", and which we call a "processor vector" or "PV". We will see that this simple structure can efficiently solve the rather difficult problems of multiplying matrices and of constructing minimum spanning trees.
This research was supported in part by the Office of Naval Research under Contract N00014-7G-C-0370 and in part by a grant from the Deutsche Forschungsgeineinschaft (DFG).
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References
Bentley, J. L. [1980]. "A parallel algorithm for constructing minimum spanning trees," to appear in the Journal of Algorithms.
Cheriton, D. and R. E. Tarjan [1976]. "Finding minimum spanning trees," SIAM J. Computing 5, 4, December 1976, pp. 724–742.
Goodman, S. E. and S. T. Hedetniemi [1977]. Introduction to the Design and Analysis of Algorithms, McGraw-Hill.
Horowitz, E. [1979]. "VLSI architecture for matrix computations," Proceedings of the 1979 International Conference on Parallel Processing, pp. 124–127, August 1979, IEEE.
Kung, H. T. [1979a]. "The structure of parallel algorithms," to appear in Advances in Computers.
Kung, H. T. [1979b]. "Let's design algorithms for VLSI systems", Caltech Conference on VLSI: Architecture, Design and Fabrication, January 1979.
Kung, H. T. and C. E. Leiserson [1980], "Systolic arrays (for VLSI)," in Mead and Conway [1980], Section 8.3.
Mead, C. A. and L. A. Conway [1980]. Introduction to VLSI Systems, Addison-Wesley, Reading Mass.
Preparata, F. P. and J. Vuillemin [1979]. "Cube-connected-cycles: A versatile network for parallel computation," Twentieth Symposium on the Foundations of Computer Science, IEEE, October 1979, pp. 140–147.
Savage, C. D. [1977]. "Parallel algorithms for graph theoretic problems," University of Illinois Coordinated Science Laboratory Report UILU-ENG-77-2231.
Sollin [1977]. An algorithm attributed to Sollin in Goodman and Hedetniemi [1977], Section 5.5. (Also referred to in Yao [1977].)
Thompson, C. D. [1979]. "Area-time complexity for VLSI," Eleventh ACM Symposium on the Theory of Computing, ACM, May 1979.
Yao, A. C. [1977]. "On constructing minimum spanning trees in k-dimensional space and related problems," Stanford Computer Science Department Report STAN-CS-77-642 (December 1977).
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Bentley, J.L., Ottmann, T. (1981). The power of a one-dimensional vector of processors. In: Noltemeier, H. (eds) Graphtheoretic Concepts in Computer Science. WG 1980. Lecture Notes in Computer Science, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10291-4_7
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DOI: https://doi.org/10.1007/3-540-10291-4_7
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