A general theory for deadlock avoidance in wormhole-routed networks

IEEE Transactions on Parallel and Distributed Systems

Volumn 9, Issue 7, 1998, Pages 626-638

  Fleury, Eric ^b   Fraigniaud, Pierre ^a,c  

^a IEEE   (France)

^b LORIA   (France)

^c UFR 919 Laboratoire d'Informatique Pour la Mécanique et les Sciences de l'Ingénieur   (France)

Author keywords

Deadlock; Multicast; Routing; Wormhole

Indexed keywords

ALGORITHMS; COMMUNICATION CHANNELS (INFORMATION THEORY); COMPUTER SYSTEM RECOVERY; CONGESTION CONTROL (COMMUNICATION); DATA COMMUNICATION SYSTEMS; DATA STORAGE EQUIPMENT; INTERCONNECTION NETWORKS; STORAGE ALLOCATION (COMPUTER);

DEADLOCK AVOIDANCE; WORMHOLE-ROUTED NETWORKS;

PARALLEL PROCESSING SYSTEMS;

EID: 0032117885     PISSN: 10459219     EISSN: None     Source Type: Journal    
DOI: 10.1109/71.707539     Document Type: Article

References (76)

1. V. Adve and M. Vernon, "Performance Analysis of Mesh Interconnection Networks with Deterministic Routing," IEEE Trans. Parallel and Distributed Systems, vol. 5, pp. 225-246, 1994.
2. K. Anjan and T. Pinkston, "An Efficient Fully Adaptive Deadlock Recovery Sceme: DISHA," Proc. 22nd Int'l Symp. Computer Architecture, pp. 201-210, 1995.
3. K. Anjan, T. Pinkston, and J. Duato, "Generalized Theory for Deadlock-Free Adaptive Routing and Its Application to DISHA," Proc. 10th Int'l Parallel Processing Symp., pp. 815-821, 1996.
4. K. Aoyama and A.A. Chien, "The Cost of Adaptativity and Virtual Lanes," J. VLSI Design, 1993.
5. 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, pp. 469-484, 1993.
6. B. Awerbuch, A. Bar-Noy, N. Linial, and D. Peleg, "Improved Routing Strategies with Succinct Tables," J. Algorithms, vol. 11, pp. 307-341, 1990.
7. A. Ben-Dor, S. Halevi, and A. Schuster, "Potential Function Analysis of Greedy Hot-Potato Routing," Proc. 13th ACM Symp. Principles Distributed Computing, pp. 225-234, 1993.
8. P. Berman, L. Gravano, G. Pifarre, and J. Sanz, "Adaptive Deadlock and Livelock Free Routing with All Minimal Paths in Torus Networks," Proc. 19th Ann. ACM Symp. Parallel Algorithms and Architectures, 1992.
9. J.-C. Bermond and C. Peyrat, "de Bruijn and Kautz Networks: A Competitor for the Hypercube?," Hypercube and Distributed Computers, F. Andre and J. Verjus, eds., pp. 279-294. North Holland, 1989.
10. J.-C. Bermond and M. Syska, "Routage Wormhole et Canaux Virtuels," Algorithmique Parallèle, M.N.M. Cosnard and Y. Robert, eds., pp. 149-158. Masson, 1992.
11. N. Biggs, Algebraic Graph Theory. London: Cambridge Univ. Press, 1974.
12. R. Boppana and S. Chalasani, "New Wormhole Routing Algorithms for Multicomputers," Proc. Seventh Int'l Parallel Processing Symp., pp. 419-423, Newport Beach, Calif., Apr. 1993.
13. C.M. Chiang and L. Ni, "Deadlock-Free Multi-Head Wormhole Routing," Proc. First High Performance Computing Asia Conf., 1995.
14. A. Chien, "A Cost and Speed Model for k-ary n-Cube Wormhole routers," Proc. Hot Interconnects '93, Palo Alto, Calif., Aug. 1993.
15. F. Chung, E. Coffman, M. Reiman, and B. Simon," The Forwarding Indices of Communication Networks," IEEE Trans. Information Theory, vol. 33, pp. 224-232, 1987.
16. R. Cypher and L. Gravano, "Adaptive, Deadlock-Free Packet Routing in Torus Networks with Minimal Storage," Proc. 1992 Int'l Conf. Parallel Processing, vol. III, pp. 204-211, Aug. 1992.
17. R. Cypher and L. Gravano, "Requirements for Deadlock-Free Adaptive Packet Routing," Proc. 11th ACM Symp. Principles of Distributed Computing, 1992.
18. W. Dally, "Virtual-Channel Flow Control," IEEE Trans. Parallel and Distributed Systems, vol. 3, pp. 194-205, 1992.
19. W. Dally and H. Aoki, "Deadlock-Free Adaptive Routing in Multicomputer Network Using Virtual Channels," IEEE Trans. Parallel and Distributed Systems, vol. 4, pp. 466-475, 1993.
20. W. Dally and C. Seitz, "The Torus Routing Chip," Distributed Computing, vol. 1, pp. 187-196, 1986.
21. W. Dally and C. Seitz, "Deadlock-Free Message Routing in Multiprocessor Interconnection Networks," IEEE Trans. Computers, vol. 36, pp. 547-553, 1987.
22. M. Di Ianni, "Wormhole Deadlock Prediction," Proc. Euro-Par '97, LNCS 1300, 1997.
23. J. Duato, "On the Design of Deadlock-Free Adaptive Routing Algorithms for Multicomputers: Design Methodologies," PARLE '91, Lecture Notes in Computer Science, pp. 390-405, June 1991.
24. J. Duato, "On the Design of Deadlock Free Adaptative Routing Algorithms for Multicomputers: Theoretical Aspects," Lecture Notes in Computer Science 487, Distributed Memory Computing, A Bode, ed., pp. 234-243. Springer Verlag, 1991.
25. J. Duato, " Channel Classes: A New Concept for Deadlock Avoidance in Wormhole Networks," Parallel Processing Letters, vol. 2, pp. 347-354, 1992.
26. J. Duato, "A New Theory of Deadlock-Free Adaptive Routing in Wormhole Networks," IEEE Trans. Parallel and Distributed Systems, vol. 4, pp. 1,320-1,331, 1993.
27. J. Duato, "On the Design of Deadlock-Free Adaptive Multicast Routing," Parallel Processing Letters, vol. 3, pp. 321-334, 1993.
28. J. Duato, "A Theory to Increase the Effective Redundancy in Wormhole Networks," Parallel Processing Letters, vols. 1 and 2, pp. 125-138, 1994.
29. J. Duato, "A Necessary and Sufficient Condition for Deadlock-Free Adaptive Routing in Wormhole Networks," IEEE Trans. Parallel and Distributed Systems, vol. 6, pp. 1,055-1,067, 1995.
30. J. Duato, "A Theory of Deadlock-Free Adaptive Multicast Routing in Wormhole Networks," IEEE Trans. Parallel and Distributed Systems, vol. 6, pp. 976-987, 1995.
31. U. Feige and P. Raghavan, "Exact Analysis of Hot Potato Routing," Proc. 33rd Ann. Symp. Foundations of Computer Science. IEEE CS Press, 1992.
32. S. Felperin, P. Raghavan, and E. Upfal, "A Theory of Wormhole Routing in Parallel Computers," Proc. 33rd Ann. IEEE Conf. Foundations of Computer Science, pp. 563-572, 1992.
33. E. Fleury and P. Fraigniaud, "Deadlocks in Adaptive Wormhole Routing," Research Report 94-09, Laboratoire de l'Informatique du Parallélisme, ENS-Lyon, France, 1994.
34. P. Fraigniaud, "Asymptotically Optimal Broadcasting and Gossiping in Faulty Hybercubes Multicomputers," IEEE Trans. Computers, vol. 41, pp. 1,410-1,419, 1992.
35. P. Fraigniaud and C. Gavoille, "Memory Requirement for Universal Routing Schemes," Proc. 14th Ann. ACM Symp. Principles of Distributed Computing (PODC), pp. 223-230, 1995.
36. P. Fraigniaud and E. Lazard, "Methods and Problems of Communication in Usual Networks," Discrete Applied Mathematics, vol. 53, pp. 79-133, 1994.
37. D. Gelernter, "A DAG-Based Algorithm for Prevention of Store-And-Forward Deadlock in Packet Networks," IEEE Trans. Computers, vol. 30, pp. 709-715, 1981.
38. C. Germain, "Etude des Mécanismes de Communication Pour une Machine Massivement Parallèle: MEGA," PhD thesis, Université Paris Sud, Orsay, France, 1989.
39. C. Glass and L. Ni, "Adaptive Routing in Mesh-Connected Networks," Proc. 12th Int'l Conf. Distributed Computing Systems, pp. 12-19, 1992.
40. C. Glass and L. Ni, "Maximally Fully Adaptive Routing in 2D Meshes," Proc. 1992 Int'l Conf. Parallel Processing, vol. I, pp. 101-104, Aug. 1992.
41. C. Glass and L. Ni, "The Turn Model for Adaptive Routing," Proc. 18th Ann. Int'l Symp. Computer Architecture, pp. 116-125, 1992.
42. C. Glass and L. Ni, "Fault-Tolerant Wormhole Routing in Meshes," Proc. 23rd Int'l Symp. Fault-Tolerant Computing, 1993.
43. C. Glass and L. Ni, "The Turn Model for Adaptive Routing," J. ACM, vol. 5, pp. 874-902, 1994.
44. W. Guan, W. Tsai, and D. Blough, "An Analytical Model for Wormhole Routing in Multicomputer Interconnection Networks," Proc. Seventh Int'l Parallel Processing Symp., pp. 650-654, Newport Beach, Calif., Apr. 1993.
45. K. Gunter, "Prevention of Deadlocks in Packet-Switched Data Transport Systems," IEEE Trans. Comm., vol. 29, pp. 512-524, 1981.
46. B. Hajek, "Bound on Evacuation Time for Deflection Routing," Distributed Computing, vol. 5, pp. 1-6, 1991.
47. S. Hedetniemi, S. Hedetniemi, and A. Liestman, "A Survey of Gossiping and Broadcasting in Communication Networks," Networks, vol. 18, pp. 319-349, 1986.
48. M.-C. Heydemann, J.-C. Meyer, and D. Sotteau, "On Forwarding Indices of Networks," Discrete Applied Mathematics, vol. 23, pp. 103-123, 1989.
49. D. Jayasimha, D. Manivannan, J. May, L. Schweibert, and S. Hary, "A Foundation for Designing Deadlock-Free Routing Algorithms in Wormhole Networks," Proc. Symp. Parallel and Distributed Processing (SPDP '96), pp. 190-197, 1996.
50. P. Kermani and L. Kleinrock, "Virtual Cut-Through: A New Computer Communication Switching Technique," Computers Networks, vol. 3, pp. 267-286, 1979.
51. T. Leighton, "Average Case Analysis of Greeding Routing Algorithms on Arrays," Proc. Second Ann. ACM Symp. Parallel Algorithms and Architectures, pp. 2-10, 1990.
52. X. Lin, P. McKinley, and L. Ni, "The Message Flow Model for Routing in Wormhole-Routed Networks," IEEE Trans. Parallel and Distributed Systems, vol. 6, pp. 755-759, 1995.
53. X. Lin and L. Ni, "Deadlock-Free Multicast Wormhole Routing in Multicomputer Networks," Proc. 18th Ann. Int'l Symp. Computer Architecture, pp. 116-125, 1991.
54. D. Linder and J. Harden, "An Adaptive and Fault Tolerant Wormhole Routing Strategy for k-ary n-Cube," IEEE Trans. Parallel and Distributed Systems, vol. 2, pp. 2-12, 1991.
55. The T9000 Products-Overview Manual, P.T.M. May and P. Welch, eds. SGS-Thomson-Inmos, 1991.
56. P. Merlin and J. Schweitzer, "Deadlock Avoidance in Store-And-Forward Networks-I: Store-And-Forward Deadlock," IEEE Trans. Comm., vol. 28, pp. 345-354, 1980.
57. J. Misic and Z. Jovanovic, "Routing Function and Deadlock Avoidance in a Star Graph Interconnection Network," J. Parallel and Distributed Computing, vol. 22, pp. 216-228, 1994.
58. L. Ni and P. McKinley, "A Survey of Wormhole Routing Techniques in Direct Networks," Computer, vol. 26, pp. 62-76, 1993.
59. P. Pacheco, Parallel Programming with MPI. Morgan Kaufmann, 1995.
60. D. Panda, S. Singal, and P. Prabhakaran, "Multidimensional Message Passing Mechanism Conforming to Base Wormhole Routing Scheme," Proc. Workshop Parallel Computer Routing and Comm., K. Holding and L. Snyder, eds., no. 853, pp. 131-145, 1994.
61. H. Park and D. Agrawal, "Generic Methodologies for Deadlock-Free Routing," Proc. 10th Int'l Parallel Processing Symp., pp. 638-643, 1996.
62. D. Peleg and E. Upfal, "A Trade-Off Between Space and Efficiency for Routing Tables," J. ACM, vol. 36, pp. 510-530, 1989.
63. J. Peters and M. Syska, "Circuit-Switched Broadcasting in Torus Networks," IEEE Trans. Parallel and Distributed Systems, vol. 7, pp. 246-266, 1996.
64. G. Pifarré, L. Gravano, S. Felperin, and C. Sanz, "Fully Adaptive Minimal Deadlock-Free Packet Routing in Hypercubes, Meshes, and Other Networks: Algorithms and Simulations," IEEE Trans. Parallel and Distributed Systems, vol. 5, pp. 247-263, 1994.
65. A. Reddy, "Fault Tolerance of Adaptive Routing Algorithms in Multicomputers," technical report, IBM Almaden Research Center, San Jose, Calif., 1992.
66. J.D. Rumeur, "Communcation dans les Réseaux de Processeurs," Collection Etudes et Recherches en Informatique. Masson, 1994.
67. M. Samatham and D. Pradhan, "The de Bruijn Multiprocessor Network: A Versatile Parallel Processing andSorting Network for VLSI," IEEE Trans. Computers, vol. 38, pp. 567-581, 1989.
68. L. Schwiebert, "Deadlock-Free Oblivious Wormhole Routing with Cyclic Dependencies," Proc. Ninth Ann. ACM Symp. Parallel Algorithms and Architectures (SPAA '97), pp. 149-158, 1997.
69. L. Schwiebert and D. Jayasimha, "A Universal Proof Technique for Deadlock-Free Routing in Interconnection Networks," Proc. Seventh Ann. ACM Symp. Parallel Algorithms and Architectures (SPAA '95), pp. 175-183, 1995.
70. L. Schwiebert and D. Jayasimha, "A Necessary and Sufficient Condition for Deadlock-Free Wormhole Routing," J. Parallel and Distributed Computing, vol. 32, pp. 103-117, 1996.
71. A. Tanenbaum, Computer Networks, pp. 15-21. Prentice Hall, 1981.
72. C. Trefftz and P. McKinley, "Performance Evaluation of Wormhole Routing in Octagonal Mesh Direct Network," Proc. Int'l Conf. Parallel and Distributed Systems, pp. 25-32, 1992.
73. E. Upfal, "On the Theory of Interconnection Networks for Parallel Computer," Proc. Int'l Colloquium on Automata, Languages, and Programming (ICALP '94), 1994.
74. L. Valiant, "A Scheme for Fast Parallel Communication," SIAM J. Computing, vol. 11, pp. 350-361, 1982.
75. V. Varavithya and P. Mohapatra, "Tree-Based Multicasting on Wormhole Routed Multistage Interconnection Networks," Proc. 1997 Int'l Conf. Parallel Processingi, 1997.
76. C. Yang and Y. Tsai, "Fault-Tolerant and Deadlock-Free Wormhole Routing in the Hybercube Network," Proc. Int'l Conf. Parallel and Distributed Systems, pp. 9-16, 1992.