Abstract
The problem to determine whether a network contains a Hamiltonian path has been a. fundamental problem in graph theory. We prove the existence of a Hamiltonian path in the Shuffle Exchange network SX(n). This problem has been posed as an open problem by Leighton in [8] and Samatham and Pradhan in [11].
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Fred Annexstein, Marc Baumslag, Arnold L. RosenbergGroup Action Graphs and Parallel Architectures. SIAM Journal of Computing, Vol 19, No 3, pp 554–569, (1990)
Hans L. BodlaenderThe Classification of Coverings of Processor Networks. Journal of Parallel and Distributed Computing 6, pp 166–182, (1989)
N. G. de BruijnA Combinatorial Problem. Indagationes Math. 8, pp 461–467, (1946)
Rainer Feldmann, Walter UngerThe Cube-Connected Cycles Network is a Subgraph of the Butterfly Network. submitted to Parallel Processing Letters, (1991)
Rainer Feldmann, Peter Mysliwietz, Stefan TschökeThe Shuffle Exchange Network of Dimension2Has a Hamiltonian Path. unpublished manuscript, 1991
E. N. GilbertGray Codes and Paths on then-Cube. Bell System Technical Journal 37, pp 815–826, (1957)
Ronald J. GouldUpdating the Hamiltonian Problem — A Survey. Journal of Graph Theory, vol. 15, no. 2, pp 121–157, (1991)
F. Thomson LeightonIntroduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes Morgan Kaufmann Publishers, Chapter 3, page 509, (1991)
Burkhard Monien, Hal SudboroughComparing Interconnection Networks. MFCS 88, pp 138–153, (1988)
Franco P. Preparata, J. VuilleminThe Cube-Connected-Cycles. A Versatile Network for Parallel Computation. IEEE FOCS vol. 20, pp140–147, (1979)
Maheswara R. Samatham, Dhiraj K. Pradhan The DeBruijn Multiprocessor Network: A Versatile Parallel Processing and Sorting Network for VLSI. IEEE Transactions on Computers vol. 20, no. 4, pp 567–581, (1989)
Alan M. Schwartz, Michael C. LouiDictionary Machines on Cube-Class Networks. IEEE Transactions on Computers vol. C-36, no. 1, pp 100–105, (1987)
Harold S. StoneParallel Processing with the Perfect Shuffle. IEEE Transactions on Computers vol. C-20, no. 2, pp 153–161, (1971)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fdelmann, R., Mysliwietz, P. (1992). The shuffle exchange network has a Hamiltonian path. In: Havel, I.M., Koubek, V. (eds) Mathematical Foundations of Computer Science 1992. MFCS 1992. Lecture Notes in Computer Science, vol 629. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-55808-X_23
Download citation
DOI: https://doi.org/10.1007/3-540-55808-X_23
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55808-8
Online ISBN: 978-3-540-47291-9
eBook Packages: Springer Book Archive