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Wait-Free Deflection Routing of Long Messages
May 2001 (vol. 12 no. 5)
pp. 476-488

Abstract—In order to obtain the lowest possible latency, routing algorithms should try to avoid a message waiting for resources (network links) blocked by other messages or multiplexing of more messages over one physical channel. This requirement becomes especially important in the case of long messages. The only type of protocols able to guarantee waiting free routing under heavy load are algorithms based on deflection (also called nonminimal adaptive or hot potato) routing. This paper deals with problems connected with the use of deflection algorithms. In contrast to the case of nonadaptive or partially (e.g., minimal) adaptive routing, it is very infrequent that an unrestricted deflection routing becomes deadlocked and, similarly, livelock is not a serious problem. On the other hand, there is another phenomenon, called a deflection jam, that limits throughput of deflection algorithms used to route long messages. It has been observed for many deflection heuristics, interconnection network topologies, and both virtual cut-through and wormhole routing. A deflection jam is a sudden and persistent saturation of a network which sometimes occur, after a very long period of undisturbed communication. This paper describes events that trigger this saturation which suggest ways to design improved and stable deflection routing algorithms.

[1] M. Ajtai, J. Komlós, and E. Szemerédi, “Largest Random Component of a$k$-Cube,” Combinatorica, vol. 2, pp. 1-7, 1982.
[2] “ATM Asynchronous Transfer Mode,” A standard of ITU-T (International Telecommunications Union-Telecommunication Sector).
[3] B. Bollobás, Random Graphs. Academic Press, 1995.
[4] A.Z. Broder, A.M. Frieze, and E. Upfal, “Existence and Construction of Edge-Disjoint Paths on Expander Graphs,” SIAM J. Computing, vol. 23, no. 5, pp. 976-989, Oct. 1994.
[5] A.Z. Broder, A.M. Frieze, S. Suen, and E. Upfal, “Optimal Construction of Edge-Disjoint Paths in Random Graphs,” Proc. Fifth ACM-SIAM Symp. Discrete Algorithms, pp. 603-612, 1994.
[6] S.B. Choi and A.K. Somani, "Rearrangeable Circuit-Switched Architectures for Routing Permutations," J. Parallel and Distributed Computing, vol. 19, no. 2, pp. 125-130, Oct. 1993.
[7] 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.
[8] 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.
[9] P. Erdos and A. Rényi, “On Evolution of Random Graphs,” Publication Math. Inst. of the Hungarian Academy Science, vol. 5, pp. 17-61, 1960.
[10] P. Erdos and J. Spencer, “Evolution of the$n$-Cube,” Computers and Math. with Applications, vol. 5, pp. 33-40, 1979.
[11] “Fibre Channel FC-PH,” Am. Nat'l Standard ANSI X3. 230.
[12] 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.
[13] HiPPI - High Performance Parallel Interface, Mechanical, Electrical, and Signalling Protocol Specification (HIPPI-PH), ANSI X3. 183-1991.
[14] N. Kahale and T. Leighton, “Greedy Dynamic Routing on Arrays,” Proc. Sixth ACM-SIAM Symp. Discrete Algorithms, pp. 558-566, 1995.
[15] J.H. Kim, Z. Liu, and A.A. Chien., "Compressionless Routing: A Framework for Fault-Tolerant Routing," IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 3, pp. 229-244, Mar. 1997.
[16] A. Karlin, G. Nelson, and H. Tamaki, “On the Fault Tolerance of the Butterfly,” Proc. 26th Ann. ACM Symp. Theory of Computing, pp. 125-133, 1994.
[17] P. Kermaniaud and L. Kleinrock, “Virtual Cutthrough: A New Computer Communication Switching Technique,” Computer Networks, vol. 3, pp. 267-286, 1979.
[18] H. Kersten, “The Critical Probability of Bond Percolation on the Square Lattice Equals 1/2,” Comm. Math. Physics, vol. 74, pp. 41-59, 1980.
[19] S. Konstatinidou and L. Snyder, “Chaos Router,” IEEE Trans. Computers, vol. 43, no. 12, pp. 1386-1397, Dec. 1994.
[20] F.T. Leighton,Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes.San Mateo, Calif.: Morgan Kaufmann, 1992.
[21] F.T. Leighton, B.M. Maggs, and S.B. Rao, “Packet Routing and Job-Shop Scheduling in$O(\hbox{congestion}+\hbox{dilation})$Steps,” Combinatorica, vol. 14, pp. 167-186, 1994.
[22] A. Lubiw, “Counterexample to a Conjecture of Szymanski on Hypercube Routing,” Information Processing Letters, vol. 35, pp. 57-61, 1990.
[23] Mathies, “Percolation Theory and Computing with Faulty Arrays of Processors,” Proc. Third ACM-SIAM Symp. Discrete Algorithms, pp. 100-103, 1992.
[24] N.F. Maxemchuk, “The Manhattan Street Network,” Proc. IEEE Globecom, pp. 255-261, Sept. 1985.
[25] F. Meyer auf der Heide and B. Vöcking, “Routing in Arbitrary Network,” Proc. 12th STACS, 1995.
[26] J. Rolim, P. Tvrdík, J. Trdlicka, and I. Vrto, “Bisecting de Bruijn and Kautz Graphs,” L.M. Kirousis and E. Kranakis, eds., Structure, Information and Comm. Complexity. Proc. Second Colloquium, Carleton Univ. Press, pp. 211-222, 1996. Discrete Applied Math., vol. 85, no. 1, pp. 87-97, 1998.
[27] A. Schwill, “Shortest Edge-Disjoint Paths in Graphs,” Proc. Sixth Ann. Symp. Theoretical Aspects of Computer Science, pp. 505-516, 1989.
[28] “SCI—Scalable Coherent Interface,” IEEE Standard 1596, 1992.
[29] A.P. Sprague and H. Tamaki, “Routing for Involutions of a Hypercube,” Discrete Applied Math., vol. 48, pp. 175-186, 1994.
[30] T. Szymanski, “On the Permutation Capability of a Circuit-Switched Hypercube,” Proc. Int'l Conf. Parallel Processing, vol. I, pp. 103-110, 1989.

Index Terms:
Deflection routing, fully adaptive routing, latency, throughput, contention.
Ludek Kucera, "Wait-Free Deflection Routing of Long Messages," IEEE Transactions on Parallel and Distributed Systems, vol. 12, no. 5, pp. 476-488, May 2001, doi:10.1109/71.926169
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