This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Adaptive Deadlock- and Livelock-Free Routing with All Minimal Paths in Torus Networks
December 1994 (vol. 5 no. 12)
pp. 1233-1251

This paper consists of two parts. In the first part, two new algorithms for deadlock- andlivelock-free wormhole routing in the torus network are presented. The first algorithm,called Channels, is for the n-dimensional torus network. This technique is fully-adaptiveminimal, that is, all paths with a minimal number of hops from source to destination areavailable for routing, and needs only five virtual channels per bidirectional link, the lowest channel requirement known in the literature for fully-adaptive minimal worm-hole routing. In addition, this result also yields the lowest buffer requirement known in the literature for packet-switched fully-adaptive minimal routing. The second algorithm, called 4-Classes, is for the bidimensional torus network. This technique is fully-adaptive minimal and requires only eight virtual channels per bidirectional link. Also, it allows for a highly parallel implementation of its associated routing node. In the second part of this paper, four worm-hole routing techniques for the two-dimensional torus are experimentally evaluated using a dynamic message injection model and different traffic patterns and message lengths.

[1] S. Borkar et al., "iWarp: An Integrated Solution to High Speed Parallel Computing,"Proc. Supercomputing 88, Vol. 1, CS Press, Los Alamitos, Calif., Order No. 882, pp. 330-339.
[2] P. Berman, L. Gravano, G.D. Pifarré, and J. L. C. Sanz, "Adaptive deadlock- and livelock-free routing with all minimal paths in torus networks," inProc. 4th Symp. Parallel Algorithms and Architectures (SPAA), 1992.
[3] Y. Birk, P. B. Gibbons, D. Soroker, and J. L. C. Sanz, "A simple mechanism for efficient barrier synchronization in MIMD machines,"RJ 7078 (67141) Comput. Sci., IBM Almaden Res. Ctr., Oct. 1989.
[4] K. Bolding and L. Snyder, "Mesh and torus chaotic routing," inMIT/Brown Advanced Res. in VLSI and Parallel Syst. Conf., Mar. 1992.
[5] F. Chong, E. Egozy, A. DeHon, and T. Knight, "Multipath fault tolerance in multistage interconnection networks,"Transit note # 48, MIT, June 1991.
[6] R. Cypher and L. Gravano, "Adantive deadlock-free packet routine in torus networks with minimal storage," inProc. ICPP 92, 1992.
[7] B. Cypher and D. Gavano, "Requirements for deadlock-free, adaptive packet routing, " inProc. 11th ACM Symp. Principles of Distrib. Computing, 1992, pp. 25-33.
[8] W. J. Dally and H. Aoki, "Adaptive routing using virtual channels," Tech. Rep., MIT, 1990.
[9] W. J. Dally, "Virtual-channel flow control," inProc. 17th Annu. Int. Symp. Comput. Architecture, May 1990.
[10] W. J. Dally and C. L. Seitz, "The torus routing chip,"Distrib. Computing, pp. 187-196, 1986.
[11] 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.
[12] W. J. Dally and P. Song, "Design of a self-timed VLSI multicomputer communication controller," inProc. Int. Conf. Comput. Design, 1987, pp. 230-234.
[13] J. Duato, "Deadlock-free adaptive routing algorithms for multicomputers: Evaluation of a new algorithm," inProc. 3rd IEEE Int. Symp. Parallel Distributed Processing, Dec. 1991.
[14] M. L. Fulgham, R. Cypher, and J. L. C. Sanz, "A comparison of SIMD hypercube routing strategies," inProc. ICPP '91, Int. Conf. Parallel Processing, 1991.
[15] S. A. Felperin, L. Gravano, G. D. Pifarré, and J. L. C. Sanz, "Fully-adaptive routing: Packet switching performance and wormhole algorithms," inSupercomputing, pp. 654-663, 1991.
[16] S. A. Felperin, L. Gravano, G. D. Pifarré, and J. L. C. Sanz, "Routing techniques for massively parallel communication,"Proc. IEEE(special issue on massively parallel computers), vol. 79, pp. 488-503, Apr. 1991.
[17] S. A. Felperin, H. Laffitte, G. Buranits, and J. L. C. Sanz, "Deadlock-free minimal packet routing in the torus network," Tech. Rep. 91-22, IBM Argentina, CRAAG, 1991.
[18] D. Gelernter, "A DAG-based algorithm for prevention of store-and-forward deadlock in packet networks,"IEEE Trans. Comput., C-30, pp. 709-715, Oct. 1981.
[19] C. J. Glass and L. M. Ni, "The turn model for adaptive routing," inProc. 19th Annu. Int. Symp. Comput. Architecture, May 1992, pp. 278-287.
[20] L. Gravano, G. D. Pifarré, S. A. Felperin, and J. L. C. Sanz, "Adaptive deadlock-free worm-hole routing with all minimal paths," Tech. Rep. 91-21, IBM Argentina, CRAAG, 1991.
[21] K. D. Gunther, "Prevention of deadlocks in packet-switched data transport systems,"IEEE Trans. Commun., vol. COM-29, no. 4, pp. 512-524, Apr. 1981.
[22] W. D. Hillis,The Connection Machine. Cambridge, MA: MIT Press, 1985.
[23] S. L. Johnsson and C. T. Ho, "Optimum broadcasting and personalized communication in hypercubes,"IEEE Trans. Comput., 38, no. 9, pp. 1249-1268, Sept. 1989.
[24] C. R. Jesshope, P. R. Miller, and J. T. Yantchev, "High performance communication in processor networks," inProc. 16th Annu. Int. Symp. Comput. Architecture, pp. 150-157, May 1989.
[25] P. Kermani and L. Kleinrock, "Virtual cut-through: A new computer communication switching technique,"Comput. Netw., vol. 3, pp. 267-286, 1979.
[26] S. Konstantinidou, "Adaptive, minimal routing in hypercubes," in6th MIT Conf. Advanced Res. VLSI, 1990, pp. 139-153.
[27] C. P. Kruskal and M. Snir, "The performance of multistage interconnection networks for multiprocessors,"IEEE Trans. Comput., vol. C-32, pp. 1091-1098, Dec. 1983.
[28] S. Konstantinidou and L. Snyder, "The Chaos router: A practical application of randomization in network routing," in2nd Ann. ACM SPAA, 1990, pp. 21-30.
[29] S. Konstantinidou and L. Snyder, "Chaos router: Architecture and performance," in18th Int. Symp. Comput. Architecture, 1991, pp. 212-221.
[30] S. Konstantinidou and E. Upfal, "Experimental comparison of multistage interconnection networks," RJ:8451 (76459), IBM Almaden Res. Ctr., Nov. 1991.
[31] T. Leighton, "Average case analysis of greedy routing algorithms on arrays," inSPAA, 1990.
[32] D. H. Linder and J. C. Harden, "An adaptive and fault tolerant wormhole routing strategy fork-aryn-cubes,"IEEE Trans. Comput., vol. 40, no. 1, pp. 2-12, Jan. 1991.
[33] D. Lenoski, J. Landon, K. Gharachorloo, W. Weber, A. Goopta, and J. Hennessy, "Overview and status of the Stanford Dash multiprocessor," inInt. Symp. Shared Memory Multiprocessing, Tokyo, Japan, Apr. 1991.
[34] T. Leighton and B. Maggs, "Expanders might be practical: Fast algorithms for routing around faults on multibutterflies," inProc. 30th Annu. IEEE Symp. Foundations Comput. Sci., 1989, pp. 384-389.
[35] T. Leighton, B. Maggs, and S. Rao, "Universal packet routing algorithms,"Proc. 29th IEEE Symp. Foundations Comput. Sci., 1988, pp. 256-269.
[36] P. M. Merlin and P. J. Schweitzer, "Deadlock avoidance in store-and-forward networks--I: Store-and-forward deadlock,"IEEE Trans. Commun., vol. COM-28, pp. 345-354, Mar. 1980.
[37] L. M. Ni and P. K. McKinley, "A survey of routing techniques in wormhole networks," MSU-CPS-ACS-46, Dep. Comput. Sci., Michigan State Univ., Oct. 1991.
[38] J. Y. Ngai and C. L. Seitz, "A framework for adaptive routing," Tech. Rep. 5246:TR:87, Dep. Comput. Sci., California Instit. Technol., 1987.
[39] J. Y. Ngai and C. L. Seitz, "Adaptive routing in multicomputers," inOpportunities and Constraints of Parallel Computing, J. L. C. Sanz, Ed. New York: Springer-Verlag, 1989.
[40] 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," inProc. 3rd Ann. ACM Symp Parallel Algorithms and Architectures, 1991.
[41] N. Pippenger, "Parallel communication with limited buffers," inFoundations of Comput. Sci., pp. 127-136, 1984.
[42] A. G. Ranade, "How to emulate shared memory," inFoundat. of Comput. Sci., pp. 185-194, 1985.
[43] A. G. Ranade, S. N. Bhat, and S. L. Johnson, "The Fluent abstract machine," in J. Allen and F. T. Leighton, Eds.,5th MIT Conf. Advanced Res. in VLSI, 1988, pp. 71-93.
[44] P. Raghavan and E. Upfal, "A theory of wormhole routing in parallel computers," Tech. Rep., IBM Res., Dec. 1991.
[45] P. Y. Song, "Design of a network for concurrent message passing systems," Master's thesis, Massachusetts Inst. of Technol., Dep. Comput. Sci., May 1988.
[46] E. Upfal, "AnO(logN) deterministic packet routing scheme," inProc. 21st Annu. ACM Symp. Theory Comput., May 1989, pp. 241-250.
[47] L. G. Valiant, "General purpose parallel architectures," inHandbook of Theoretical Computer Science, J. van Leeuwen, Ed. Amsterdam, The Netherlands: North-Holland, 1988.

Index Terms:
Index Termsconcurrency control; multiprocessor interconnection networks; performance evaluation;adaptive deadlock-free routing; livelock-free routing; minimal paths; torus networks;Channels; n-dimensional torus network; virtual channels; buffer requirement;packet-switched fully-adaptive minimal routing; 4-Classes; dynamic message injectionmodel; traffic patterns; message lengths
Citation:
L. Gravano, G.D. Pifarré, P.E. Berman, J.L.C. Sanz, "Adaptive Deadlock- and Livelock-Free Routing with All Minimal Paths in Torus Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 12, pp. 1233-1251, Dec. 1994, doi:10.1109/71.334898
Usage of this product signifies your acceptance of the Terms of Use.