This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Necessary and Sufficient Condition for Deadlock-Free Routing in Cut-Through and Store-and-Forward Networks
August 1996 (vol. 7 no. 8)
pp. 841-854

Abstract—This paper develops the theoretical background for the design of deadlock-free adaptive routing algorithms for virtual cut-through and store-and-forward switching. This theory is valid for networks using either central buffers or edge buffers. Some basic definitions and three theorems are proposed, developing conditions to verify that an adaptive algorithm is deadlock-free, even when there are cyclic dependencies between routing resources. Moreover, we propose a necessary and sufficient condition for deadlock-free routing. Also, a design methodology is proposed. It supplies fully adaptive, minimal and non-minimal routing algorithms, guaranteeing that they are deadlock-free.

The theory proposed in this paper extends the necessary and sufficient condition for wormhole switching previously proposed by us. The resulting routing algorithms are more flexible than the ones for wormhole switching. Also, the design methodology is much easier to apply because it automatically supplies deadlock-free routing algorithms.

[1] A. Agarwal, "Limits on Interconnection Network Performance," IEEE Trans. Parallel and Distributed Systems, vol. 2, no. 4, pp. 398-412, Oct. 1991.
[2] A. Arruabarrena, R. Beivide, C. Izu, and J. Miguel, "A Performance Evaluation of Adaptive Routing in Bidimensional Cut-Through Networks," Parallel Processing Letters, vol. 3, no. 4, pp. 469-489, 1993.
[3] W.C. Athas and C.L. Seitz, “Multicomputers: Message-Passing Concurrent Computers,” Computer, vol. 21, pp. 9-24, Aug. 1988.
[4] K.W. Bolding and L. Snyder, "Mesh and Torus Chaotic Routing," Proc. MIT/Brown Conf. Advanced Research in VLSI, 1992.
[5] W. Chou, A.W. Bragg, and A.A. Nilsson, "The Need for Adaptive Routing in the Chaotic and Unbalanced Traffic Environment," IEEE Trans. Commun., vol. COM-29, no. 4, pp. 481-490, Apr 1981.
[6] R. Cypher and L. Gravano, "Requirements for Deadlock-Free, Adaptive Packet Routing," Proc. 11th ACM Symp. Principles Distributed Computing, 1992.
[7] R. Cypher and L. Gravano, "Adaptive, Deadlock-Free Packet Routing in Torus Networks with Minimal Storage," Proc. Int'l Conf. Parallel Processing, Aug. 1992.
[8] W.J. Dally and C.L. Seitz, "The Torus Routing Chip," Distributed Computing, vol. 1, no. 3, pp. 187-196, Oct. 1986.
[9] 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.
[10] J. Duato, “On the Design of Deadlock-Free Adaptive Routing Algorithms for Multicomputers: Design Methodologies,” Proc. Parallel Architectures and Languages Europe 91, June 1991.
[11] 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.
[12] J. Duato and P. López, "Performance Evaluation of Adaptive Routing Algorithms for k-ary n-cubes," Proc. Workshop Parallel Computer Routing and Communication, May. 1994.
[13] J. Duato, "A Necessary and Sufficient Condition for Deadlock-Free Adaptive Routing in Wormhole Networks," Proc. Int'l Conf. Parallel Processing, Aug. 1994.
[14] 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.
[15] P.T. Gaughan and S. Yalamanchili, “Adaptive Routing Protocols for Hypercube Interconnection Networks,” Computer, vol. 26, no. 5, pp. 12–23, May 1993.
[16] D. Gelernter, "A DAG-Based Algorithm for Prevention of Store-and-Forward Deadlock in Packet Networks," IEEE Trans Computers, vol. 30, pp. 709-715, Oct. 1981.
[17] C. Germain-Renaud, "Etude des mécanismes de communication pour une machine massivement parallèle: MEGA," Ph.D. Dissertation, Univ. de Paris-Sud, Centre d'Orsay, 1989.
[18] C.J. Glass and L.M. Ni, "The Turn Model for Adaptive Routing," Proc. 19th Int'l Symp. Computer Architecture, vol. 20, no. 2, pp. 278-287, May 1992.
[19] I.S. Gopal, "Prevention of Store-and-Forward Deadlock in Computer Networks," IEEE Trans. Commun., vol. 33, no. 12, pp. 1,258-1,264, Dec. 1985.
[20] A.G. Greenberg and B. Hajek, "Deflection Routing in Hypercube Networks," IEEE Trans. Comm., vol. 35, no. 6, pp. 1,070-1,081, June 1992.
[21] K.D. Gunther, "Prevention of Deadlocks in Packet-Switched Data Transport Systems," IEEE Trans. Commun., vol. 29, pp. 512-524, Apr. 1981.
[22] P.A.J. Hilbers and J.J. Lukkien, "Deadlock-Free Message Routing in Multicomputer Networks," Distributed Computing, vol. 3, pp. 178-186, 1989.
[23] P. Kermani and L. Kleinrock, "Virtual Cut-Through: A New Computer Communication Switching Technique," Computer Networks, vol. 3, pp. 267-286, 1979.
[24] C.K. Kim and D.A. Reed, "Adaptive Packet Routing in a Hypercube," Proc. 3rd Conf. on Hypercube Concurrent Computers&Applications, Jan. 1988.
[25] S. Konstantinidou and L. Snyder, "The Chaos Router: A Practical Application of Randomization in Network Routing," Proc. 2nd ACM Symp. Parallel Algorithms Architectures, 1990.
[26] S. Konstantinidou and L. Snyder, "Chaos Router: Architecture and Performance," Proc. 18th Ann. Int'l Symp. Computer Architecture, 1991.
[27] S. Konstantinidou and L. Snyder, "The Chaos Router," IEEE Trans. Computers, vol. 43, no. 12, pp. 1,386-1,397, Dec. 1994.
[28] P.M. Merlin and P.J. Schweitzer, "Deadlock Avoidance in Store-and-Forward Networks-I: Store-and-Forward Deadlock," IEEE Trans. Commun., vol. 28, no. 3, pp. 345-354, Mar. 1980.
[29] J.Y. Ngai and C.L. Seitz, "A Framework For Adaptive Routing in Multicomputer Networks," Proc. ACM Symp. Parallel Algorithms Architectures, 1989.
[30] T. Nguyen and L. Snyder, "Performance of Minimal Adaptive Routers," Proc. Parallel Computer Routing and Communication Workshop, May 1994.
[31] 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.
[32] A.G. Nowatzyk, M.C. Browne, E.J. Kelly, and M. Parkin, "S-Connect: From Networks of Workstations to Supercomputer Performance," Proc. 22nd Int'l Symp. Computer Architecture, June 1995.
[33] G.D. Pifarré, L. Gravano, S.A. Felperin, and J.L.C. Sanz, "Fully-Adaptive Minimal Deadlock-Free Packet Routing in Hypercubes, Meshes and Other Networks," Proc. 3rd ACM Symp. Parallel Algorithms Architectures, June 1991.
[34] G.D. Pifarré, L. Gravano, S.A. Felperin, and J.L.C. Sanz, "Fully Adaptive Minimal Deadlock-Free Packet Routing in Hypercubes, Meshes and Other Networks: Algorithms and Simulations," IEEE Trans. Parallel Distributed Systems, vol. 5, no. 3, pp. 247-263, Mar. 1994.
[35] S. Ragupathy, M.R. Leutze, and S.R. Schach, "Message Routing Schemes in a Hypercube Machine," Proc. 3rd Conf. Hypercube Concurrent Computers&Applications, Jan. 1988.
[36] J. Rexford and K.G. Shin, "Support for Multiple Classes of Traffic in Multicomputer Routers," Proc. Parallel Computer Routing and Communication Workshop, May 1994.
[37] A.W. Roscoe, "Routing Messages Through Networks: An Exercise in Deadlock Avoidance," Oxford Univ. Computing Laboratory Report, 1987.
[38] A. Tanenbaum, Computer Networks. Prentice Hall, 1988.

Index Terms:
Adaptive routing, deadlock avoidance, design methodologies, interconnection networks, store-and-forward, virtual cut-through.
Citation:
José Duato, "A Necessary and Sufficient Condition for Deadlock-Free Routing in Cut-Through and Store-and-Forward Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 8, pp. 841-854, Aug. 1996, doi:10.1109/71.532115
Usage of this product signifies your acceptance of the Terms of Use.