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A Tight Lower Bound on the Number of Channels Required for Deadlock-Free Wormhole Routing
October 1998 (vol. 47 no. 10)
pp. 1158-1160

Abstract—Wormhole routing is widely employed in current generation multicomputers and the design of deadlock-free wormhole routing algorithms is an important problem. In this note, we prove a tight lower bound on the number of channels required by a broad class of deadlock-free wormhole routing algorithms. This result has applications in proving that certain topologies do not admit deadlock-free wormhole routing algorithms, as well as applications in the design and analysis of fault-tolerant wormhole routing algorithms.

[1] R. Boppana and S. Chalasani, "Fault-Tolerant Wormhole Routing Algorithms for Mesh Networks," IEEE Trans. Computers, vol. 44, no. 7, pp. 848-864, July 1995.
[2] W.J. Dally and C.L. Seitz, “Deadlock-Free Message Routing in Multiprocessor Interconnection Networks,” IEEE Trans. Computers, Vol. C-36, No. 5, May 1987, pp. 547-553.
[3] J. Duato, “A Necessary and Sufficient Condition for Deadlock-Free Adaptive Routing in Wormhole Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 10, pp. 1,055–1,067, Oct. 1995.
[4] J. Duato, "A New Theory of Deadlock-Free Adaptive Routing in Wormhole Networks," IEEE Trans. Parallel and Distributed Systems, vol. 4, no. 12, pp. 1,320-1,331, Dec. 1993.
[5] J. Duato, B. Dao, P. Gaughan, and S. Yalamanchili, "Scouting: Fully Adaptive, Deadlock-Free Routing in Faulty Pipelined Networks," Proc. 1994 Int'l Conf. Parallel and Distributed Systems, pp. 608-613, Dec. 1994.
[6] P.T. Gaughan and S. Yalamanchili, "A Family of Fault-Tolerant Routing Protocols for Direct Multiprocessor Networks," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 6, pp. 482-487, May 1995.
[7] C.J. Glass and L.M. Ni, "Fault-Tolerant Wormhole Routing in Meshes," Proc. 23rd Int'l Symp. Fault-Tolerant Computing, pp. 240-249, 1993.
[8] R. Libeskind-Hadas and E. Brandt, "Origin-Based Fault-Tolerant Routing in the Mesh," Future Generation Computer Systems, vol. 11, no. 6, pp. 603-615, Oct. 1995.
[9] L.M. Ni and P.K. McKinley, "A Survey of Wormhole Routing Techniques in Direct Networks," Computer, vol. 26, no. 2, pp. 62-76, Feb. 1993.
[10] L. Schwiebert and D.N. Jayasimha, "A Necessary and Sufficient Condition for Deadlock-Free Wormhole Routing," J. Parallel and Distributed Computing, vol. 32, no. 1, pp. 103-117, Jan. 1996.

Index Terms:
Wormhole routing, deadlock-free routing algorithms, fault tolerance.
Citation:
Ran Libeskind-Hadas, "A Tight Lower Bound on the Number of Channels Required for Deadlock-Free Wormhole Routing," IEEE Transactions on Computers, vol. 47, no. 10, pp. 1158-1160, Oct. 1998, doi:10.1109/12.729799
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