Abstract
The Algebraic Path Problem is a general framework which unifies several algorithms arising from various fields of computer science. Rote [11] introduces a general algorithm to solve any instance of the APP, as well as a hexagonal systolic array of (n+1)2 elementary processors which can solve the problem in 7n-2 time steps. We propose a new algorithm to solve the APP, and demonstrate its equivalence with Rote's algorithm. The new algorithm is more suitable to parallelization: we propose an orthogonal systolic array of n(n+1) processors which solves the APP within only 5n-2 steps. Finally, we give some experiments on the implementation of our new algorithm in the parallel environment developped by IBM at ECSEC in Roma.
Support from the IBM European Center for Scientific and Engineering Computing in Roma and the Coordinated Research Program C3 of CNRS is gratefully acknowledged.
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References
E. CLEMENTI, Progress report on our experimentation with parallel supercomputers ICAP1 and ICAP2, Conf. "Le Calcul ... Demain", P. Chenin et al. eds, Masson 1985
P. DI CHIO, V. ZECCA, IBM ECSEC facilities: user's guide, IBM ECSEC Report, Roma 1985
L.J. GUIBAS, H.T. KUNG, C.D. THOMPSON, Direct VLSI implementation of combinatorial algorithms, Proc. Caltech Conf. on VLSI, California Inst. Technology, Pasadena 1979, 509–525
K. HWANG et F. BRIGGS, Parallel processing and computer architecture, Mc Graw Hill, 1984
H.T. KUNG, Why systolic architectures, Computer 15, 1 (1982), 37–46
H.T. KUNG, C.E. LEISERSON, Systolic arrays for (VLSI), Proc. of the Symposium on Sparse Matrices Computations, I.S. Duff and G.W. Stewart eds, Knoxville, Tenn. (1978), 256–282
R.E. LORD, J.S. KOWALIK, S.P. KUMAR, Solving linear algebraic equations on an MIMD computer, J. ACM 30 (1), (1983), p 103–117
J.G. NASH, S. HANSEN, G.R. NUDD, VLSI processor arrays for matrix manipulation, VLSI Systems & Computations, H.T.Kung et al. eds, Computer Science Press (1981), 367–378
Y. ROBERT, Block LU decomposition of a band matrix on a systolic array, Int. J. Computer Math. 17 (1985), 295–315
Y. ROBERT, D. TRYSTRAM, Un réseau systolique pour le problème du chemin algébrique, C.R.A.S. Paris 302, I, 6 (1986), 241–244
G. ROTE, A systolic array algorithm for the algebraic path problem (shortest paths; matrix inversion), Computing 34 (1985), 191–219
U. SCHENDEL, Introduction to numerical methods for parallel computers, E. Horwood 1984
J.M. STONE, V.A. NORTON, F.D. ROGERS, E.A. MELTON, G.F. PFISTER, The VM/EPEX FORTRAN preprocessor reference, IBM Report, Yorktown Heights, NY, USA (1985)
U. ZIMMERMANN, Linear and combinatorial optimization in ordered algebraic structures, Ann. Discrete Math. 10, 1 (1981), 1–380
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© 1986 Springer-Verlag Berlin Heidelberg
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Robert, Y., Trystram, D. (1986). Parallel implementation of the algebraic path problem. In: Händler, W., Haupt, D., Jeltsch, R., Juling, W., Lange, O. (eds) CONPAR 86. CONPAR 1986. Lecture Notes in Computer Science, vol 237. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16811-7_165
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DOI: https://doi.org/10.1007/3-540-16811-7_165
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