DCC linear congruential graphs: A new class of interconnection networks

IEEE Transactions on Computers

Volumn 45, Issue 2, 1996, Pages 156-164

  Opatrny, J ^b   Sotteau, D ^c   Srinivasan, N ^d   Thulasiraman, K ^a,e  

^a IEEE

^b Dept of Electrical and Computer Engineering   (Canada)

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

^d Agurchand Manmull Jain College   (India)

^e University of Oklahoma   (United States)

Author keywords

Computer networks; Graph theory; Interconnectons networks; Network design; Parallel processing

Indexed keywords

EID: 0002557526     PISSN: 00189340     EISSN: None     Source Type: Journal    
DOI: 10.1109/12.485369     Document Type: Article

References (29)

1. S.B. Akers and B. Krishnamurthy, "A group-theoretic model for symmetric interconnection networks," IEEE Trans. Computers, vol. 38, no. 4, pp. 555-566, Apr. 1989.
2. B.W. Arden and H. Lee, "Analysis of chordal ring network," IEEE Trans. Computers, vol. 30, no. 4, pp. 291-295, Apr. 1981.
3. J.C. Bermond and B. Bollobas, "The diameter of graphs - a survey," Proc. Congressus Numerantium, vol. 32, pp. 3-27, 1981.
4. J.C. Bermond, F. Comellas, and D.F. Hsu, "Distributed loop computer networks, (a survey)," J. Parallel and Distributed Computing, to appear.
5. J.C. Bermond, C. Delorme, and G. Farhi, "Large graphs with given degree and diameter III," Proc. Coll. Cambridge (1981).
6. Ann. Discrete Math. 13, North-Holland, pp. 23-32, 1982.
7. J.C. Bermond, C. Delorme, and J.J. Quisquater, "Strategies for interconnection networks: some methods from graph theory," J. Parallel and Distributed Computing, vol. 3, pp. 433-449, 1986.
8. J.C. Bermond, N. Homobono, and C. Peyrat, "Large fault-tolerant interconnection networks," First Japan Conf. Graph Theory and Applications, Hakone, Japan, June 1986.
9. J.C. Bermond and C. Peyrat, "deBruijn, and Kautz networks: A competitor for the hypercube?" Proc. Conf. Hypercube and Distributed Computers, pp. 279-294, 1989.
10. B. Bollobas and W.F. de la Vega, "The diameter of random graphs," Combinatorial 2, pp. 125-134, 1982.
11. J.A. Bondy and U.S.R. Murty, Graph Theory with Applications. North Holland, 1976.
12. N.G. deBruijn, "A combinatorial problem," Koninklije Nedderlandse Academie van Wetenshappen Proc., vol. ser A49, pp. 758-764, 1946.
13. F.R.K. Chung, "Diameters of graphs: Old problems and new results," Proc. 18th South-Eastern Conf. Combinatorics, Graph Theory, and Computing, Congressus Numerantium, pp. 295-317, 1987.
14. C. Delorme, "A table of large graphs of small degrees and diameters," personnal communication, 1990.
15. D.Z. Du and F.K. Hwang, "Generalized de Bruijn digraphs," Networks, vol. 18, pp. 28-38, 1988.
16. D.Z. Du, D.F. Hsu, and G.W. Peck, "Connectivity of consecutive-d digraphs," Discrete Applied Math., to appear.
17. B. Elpas, "Topological constraints on interconnection limited logic," Switching Circuits Theory and Logical Design 5, pp. 133-147, 1964.
18. D.M. Gordon, "Parallel sorting on Cayley graphs, abstract," The Capital City Conf. Combinatorics and Theoretical Computer Science, May 1989.
19. W.D. Hillis, The Connection Machine. Cambridge, Mass.: MIT Press, 1987.
20. M. Imase and M. Itoh, "Design to minimize diameter on building block network," IEEE Trans. Computers, vol. 30, pp. 439-442, 1981.
21. M. Jerrum and S. Skyum, "Families of fixed degree graphs for processor interconnection," IEEE Trans. Computers, vol. 33, pp. 190-194, 1984.
22. W.H. Kautz, "Bounds on directed (d, k) graphs," Theory of Cellular Logic Networks and Machines, SRI Project 7258, pp. 20-28, 1968.
23. M. Klawe, "Limitations on explicit constructions of expanding graphs," Siam J. Computing, vol. 13, no. 1, pp. 156-166, 1984.
24. D.E. Knuth, The Art of Computer Programming, Seminumerical Algorithms, vol. II. Addison-Wesley, 1972.
25. W. Leland and M. Solomon, "Dense trivalent graphs for processor interconnection," IEEE Trans. Computers, vol. 31, no. 3, pp. 219-222, Mar. 1982.
26. J. Opatrny and D. Sotteau, "Linear congruential graphs, graph theory, combinatorics, algorithms, and applications," SIAM Proc. series, pp. 404-426, 1991.
27. D.K. Pradhan, Fault-Tolerant Multiprocessor and VLSI Based Systems Communication Architecture, Fault-Tolerant Computing, Theory and Techniques vol. 2. Prentice-Hall, 1986.
28. M.R. Samantham and D.K. Pradhan, "The deBruijn multiprocessor network: A versatile parallel processing and sorting network for VLSI," IEEE Trans. Computers, vol. 38, no. 4, pp. 567-581, 1989.
29. M.R. Samantham and D.K. Pradhan, "Correction to The de Bruijn multiprocessor network: A versatile parallel processing and sorting network for VLSI," IEEE Trans. Computers, vol. 40, no. 1, p. 122, Jan. 1991.