Abstract
We derive an efficient linear simd architecture for the algebraic path problem (APP). For a graph with n nodes, our array has n processors, each with 3n memory cells, and computes the result in 3n 2 - 2n steps. Our array is ideally suited for VLSI, since the controls is simple and the memory can be implemented as fifos. I/O is straightforward, since the array is linear. It can be trivially adapted to run in multiple passes, and moreover, this version improves the work efficiency. For any constant a, the running time on n/a processors is no more than (a+2)n 2. The work is no more than (1+ 2/a)n 3 and can be made as close to n 3 as desired by increasing a.
Chapter PDF
Keywords
References
A. Benaini, P. Quinton, Y. Robert, Y. Saouter, and B. Tourancheau. Synthesis of a new systolic architecture for the algebraic path problem. Science of Computer Programming. 15:135–158, 1990.
A. Benaini and Y. Robert. Space-time minimal systolic arrays for gaussian elimination and the algebraic path problem. In ASAP 90: International Conference on Application Specific Array Processors, pages 746–757, Princeton, NJ, September 1990. IEEE Press.
P.Y. Chang and J.C. Tsay. A family of efficient regular arrays for the algebraic path problem. IEEE Transactions on Computers, 43(7):769–777, July 1994.
P. Clauss, C. Mongenet, and G-R. Perrin. Synthesis of size-optimal toroidal arrays for the algebraic path problem: A new contribution. Parallel Computing, 18:185–194, 1992.
L. Guibas, H.T. Kung, and Clark D. Thompson. Direct VLSI implementation of combinatorial algorithms. In Proc. Conference on Very Large Scale Integration: Architecture, Design and Fabrication, pages 509–525, January 1979.
S.Y. Kung and S.C. Lo. A spiral systolic algorithm/architecture for transitive closure problems. In ICCD 85: International Conference on Circuit Design, pages 622–626, Rye Town, NY, 1985. IEEE.
S.Y. Kung, S.C. Lo, and P.S. Lewis. An op timal systolic design for the transitive closure and the shortest path problems. IEEE Transactions on Computers, C-36(5):603–614, May 1987.
J.F. Myoupo and C. Fabret. A modular systolic linearization of the warshall-floyd algorithm. IEEE Transactions on Parallel and Distributed Systems, 7(5):449–455, may 1996.
J.G. Nash and S. Hansen. Modified faddeew algorithm for matrix multiplication. In Proc., SPIE Workshop on Real-Time Signal Processing, pages 39–46. SPIE, 1984.
V.K. Prasanna Kumar and Y-C Tsai. Designing linear systolic arrays. Journal of Parrallel and Distributed Computing, (7):441–463, may 1989.
S.V. Rajopadhye. An improved systolic algorithm for the algebraic path problem. INTEGRATION: The VLSI Journal, 14(3):279–296, Feb 1993.
T. Risset and Y. Robert. Synthesis of processors arrays for the algebraic path problem: Unifying old results and deriving new architectures. Parallel Processing Letters, 1:19–28, 1991.
Y. Robert and M. Tchuent. FrRsolution systolique de systmes linaires denses. RAIRO Modlisation et Analyse Numrique, Technique et Sciences Informatiques, 19(2):315–326, 1985.
Y. Robert and D. Trystam. Systolic solution of the algebraic path problem. In W. Moore, A. McCabe, and R. Urquhart, editors, Systolic Arrays, 1, pages 171–180, Oxford, UK, 1987. Adam Hilger.
Günter Rote. A systolic array algorithm for the algebraic path problem (shortest paths; matrix inversion). Computing, 34(3):191–219, 1985.
Chris J. Schieman and Peter R. Cappello. A processor-time minimal systolic array for transitive closure. In International Conference on Application Specific Array Processors, pages 19–30, Princeton, NJ, September 1990. IEEE Computer Society, IEEE Computer Society Press.
T. Takaoka and K. Umehara. An efficient VLSI circuit for the all pairs shortest path problem. Journal of Parallel and Distributed Computing, 16:265–270, 1992.
C. Tayou Djamegni, P. Quinton, S. Rajopadhye, and T. Risset. Derivation of systolic algorithms for the algebraic path problem by recurrence transformations. Parallel Computing, To appear, 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rajopadhye, S., Tadonki, C., Risset, T. (1999). The Algebraic Path Problem Revisited. In: Amestoy, P., et al. Euro-Par’99 Parallel Processing. Euro-Par 1999. Lecture Notes in Computer Science, vol 1685. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48311-X_99
Download citation
DOI: https://doi.org/10.1007/3-540-48311-X_99
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66443-7
Online ISBN: 978-3-540-48311-3
eBook Packages: Springer Book Archive