Abstract
We present randomized and deterministic algorithms for many-to-one routing on an n-node two-dimensional mesh under the store-and-forward model. We consider a general instance of the problem, where each node is source (resp., destination) of l (resp., k) packets, for arbitrary values of l and k. All our algorithms run in optimal O (√lkn) time and use queues of only constant size at each node to store packets in transit. The randomized algorithms, however, are simpler to implement. Our result closes a gap in the literature, where time-optimal algorithms using constant-size queues were known only for the special cases l = 1 and l = k.
This work was supported, in part, by CNR and MURST of Italy under projects Multicast Techniques with Applications to Robotics and Packet Routing and Algorithms for Large Data Sets: Science and Engineering.
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References
S. Felperin, P. Raghavan, and E. Upfal. A theory of wormhole routing in parallel computers. IEEE Trans. on Computers, C-45(6):704–713, June 1996.
M. D. Grammatikakis, D. F. Hsu, M. Kraetzel, and J. F. Sibeyn. Packet routing in fixed-connection networks: A survey. Journal of Parallel and Distributed Computing, 54(2):77–132, November 1998.
T. Hagerup and C. Rüb. A guided tour of Chernoff bounds. Information Processing Letters, 33(6):305–308, February 1990.
K. T. Herley, A. Pietracaprina, and G. Pucci. One-to-many routing on the mesh. In Proc. of the 13th Symp. on Parallel Algorithms and Architectures, June 2001. To appear.
P. Kermani and L. Kleinrock. Virtual cut through: a new computer communication switching technique. Computer Networks, 3(4):267–286, April 1979.
F. T. Leighton. Introduction to Parallel Algorithms and Architectures: Arrays • Trees • Hypercubes. Morgan Kaufmann, San Mateo, CA, 1992.
F. Makedon and A. Symvonis. Optimal algorithms for the many-to-one routing problem on two-dimensional meshes. Microprocessors and Microsystems, 17:361–367, 1993.
I. Newman and A. Schuster. Hot-potato worm routing via store-and-forward packet routing. Journal of Parallel and Distributed Computing, 30(1):76–84, January 1995.
J. F. Sibeyn and M. Kaufmann. Deterministic 1-k routing on meshes, with application to hot-potato worm-hole routing. In Proc. of the 11th Symp. on Theoretical Aspects of Computer Science, pages 237–248, March 1994.
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© 2001 Springer-Verlag Berlin Heidelberg
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Pietracaprina, A., Pucci, G. (2001). Optimal Many-to-One Routing on the Mesh with Constant Queues. In: Sakellariou, R., Gurd, J., Freeman, L., Keane, J. (eds) Euro-Par 2001 Parallel Processing. Euro-Par 2001. Lecture Notes in Computer Science, vol 2150. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44681-8_92
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DOI: https://doi.org/10.1007/3-540-44681-8_92
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