About this Journal Submit a Manuscript Table of Contents
International Journal of Distributed Sensor Networks
Volume 2012 (2012), Article ID 124245, 15 pages
http://dx.doi.org/10.1155/2012/124245
Research Article

Distributed and Fault-Tolerant Routing for Borel Cayley Graphs

1Department of Electrical & Computer Engineering, Stony Brook University, SUNY, Stony Brook, NY 11794-2350, USA
2AT&T Labs, USA

Received 3 April 2012; Revised 25 July 2012; Accepted 8 August 2012

Academic Editor: Yanmin Zhu

Copyright © 2012 Junghun Ryu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. N. Sivarajan and R. Ramaswami, “Lightwave networks based on de Bruijn graphs,” IEEE/ACM Transactions on Networking, vol. 2, no. 1, pp. 70–79, 1994. View at Publisher · View at Google Scholar · View at Scopus
  2. K. Zhu and B. Mukherjee, “Traffic grooming in an optical WDM mesh network,” IEEE Journal on Selected Areas in Communications, vol. 20, no. 1, pp. 122–133, 2002. View at Publisher · View at Google Scholar · View at Scopus
  3. R. Duncan, “Survey of parallel computer architectures,” Computer, vol. 23, no. 2, pp. 5–16, 1990. View at Publisher · View at Google Scholar · View at Scopus
  4. R. D'Andrea and G. E. Dullerud, “Distributed control design for spatially interconnected systems,” IEEE Transactions on Automatic Control, vol. 48, no. 9, pp. 1478–1495, 2003. View at Publisher · View at Google Scholar · View at Scopus
  5. J. Sun and E. Modiano, “Capacity provisioning and failure recovery for Low Earth Orbit satellite constellation,” International Journal of Satellite Communications and Networking, vol. 21, no. 3, pp. 259–284, 2003. View at Publisher · View at Google Scholar · View at Scopus
  6. T. Bjerregaard and S. Mahadevan, “A survey of research and practices of network-on-chip,” ACM Computing Surveys, vol. 38, no. 1, pp. 71–121, 2006. View at Scopus
  7. H. Moussa, A. Baghdadi, and M. Jézéquel, “Binary de Bruijn interconnection network for a flexible LDPC/turbo decoder,” in Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS '08), pp. 97–100, May 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. A. El Gamal, “Trends in CMOS image sensor technology and design,” in Proceedings of the IEEE International Devices Meeting (IEDM '02), pp. 805–808, December 2002. View at Scopus
  9. M. Mirza-Aghatabar, S. Koohi, S. Hessabi, and M. Pedram, “An empirical investigation of mesh and torus NoC topologies under different routing algorithms and traffic models,” in Proceedings of the 10th Euromicro Conference on Digital System Design Architectures, Methods and Tools (DSD '07), pp. 19–26, IEEE Computer Society, Washington, DC, USA, August 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. E. Noel and W. Tang, “Novel sensor MAC protocol applied to cayley and manhattan street networks with cross bow MICA2,” in Proceedings of the 3rd Annual IEEE Communications Society on Sensor and Ad Hoc Communications and Networks (SECON '06), vol. 2, pp. 626–631, September 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. A. A. Taleb, J. Mathew, and D. K. Pradhan, “Fault diagnosis in multi layered De Bruijn based architectures for sensor networks,” in Proceedings of the 8th IEEE International Conference on Pervasive Computing and Communications Workshops (PERCOM '10), pp. 456–461, April 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. E. K. Lua, J. Crowcroft, M. Pias, R. Sharma, and S. Lim, “A survey and comparison of peer-to-peer overlay network schemes,” IEEE Communications Surveys &Tutorials, vol. 7, no. 2, pp. 72–793, 2005.
  13. I. Stoica, R. Morris, D. Karger, M. F. Kaashoek, and H. Balakrishnan, “Chord: a scalable peer-to-peer lookup service for internet applications,” in Proceedings of the conference on Applications, Technologies, Architectures, and Protocols for Computers Communications (ACM SIGCOMM '01), pp. 149–160, ACM, New York, NY, USA, August 2001. View at Publisher · View at Google Scholar · View at Scopus
  14. M. F. Kaashoek and D. R. Karger, “Koorde: a simple degree-optimal distributed hash table,” in Proceedings of the International Peer-to-Peer Symposium (IPTPS '03), 2003.
  15. M. Naor and U. Wieder, “Novel architectures for P2P applications: the continuous-discrete approach,” ACM Transactions on Algorithms, vol. 3, no. 3, article 34, 2007. View at Publisher · View at Google Scholar · View at Scopus
  16. D. Loguinov, J. Casas, and X. Wang, “Graph-theoretic analysis of structured peer-to-peer systems: routing distances and fault resilience,” IEEE/ACM Transactions on Networking, vol. 13, no. 5, pp. 1107–1120, 2005. View at Publisher · View at Google Scholar · View at Scopus
  17. C. Qu, W. Nejdl, and M. Kriesell, “Cayley dhts—a group-theoretic framework for analyzing dhts based on cayley graphs,” in Proceedings of the International Symposium on Parallel and Distributed Processing and Applications (ISPA '04), Springer, 2004.
  18. G. Barrenetxea, B. Berefull-Lozano, and M. Vetterli, “Lattice networks: capacity limits, optimal routing, and queueing behavior,” IEEE/ACM Transactions on Networking, vol. 14, no. 3, pp. 492–505, 2006. View at Publisher · View at Google Scholar · View at Scopus
  19. S. B. Akers and B. Krishnamurthy, “Group-theoretic model for symmetric interconnection networks,” IEEE Transactions on Computers, vol. 38, pp. 555–566, 1992. View at Scopus
  20. K. W. Tang and B. W. Arden, “Representations of borel cayley graphs,” SIAM Journal on Discrete Mathematics, vol. 6, pp. 655–676, 1993.
  21. J. C. Bermond, C. Delorme, and J. J. Quisquater, “Strategies for interconnection networks: some methods from graph theory,” Journal of Parallel and Distributed Computing, vol. 3, no. 4, pp. 433–449, 1986. View at Scopus
  22. M. Miller and J. Siran, “Moore graphs and beyond: a survey of the degree/diameter problem,” Electronic Journal of Combinatorics, vol. 14, 2009. View at Scopus
  23. G. Panchapakesan and A. Sengupta, “On a lightwave network topology using Kautz digraphs,” IEEE Transactions on Computers, vol. 48, no. 10, pp. 1131–1137, 1999. View at Scopus
  24. J. Díaz, J. Petit, and M. Serna, “A survey of graph layout problems,” ACM Computing Surveys, vol. 34, no. 3, pp. 313–356, 2002. View at Publisher · View at Google Scholar · View at Scopus
  25. K. W. Tang and B. W. Arden, “Vertex-transitivity and routing for Cayley graphs in GCR representations,” in Proceedings of the ACM/SIGAPP Symposium on Applied Computing (SAC '92), pp. 1180–1187, ACM, New York, NY, USA, March 1992. View at Scopus
  26. R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520–1533, 2004. View at Publisher · View at Google Scholar · View at Scopus
  27. J. Yu, E. Noel, and K. W. Tang, “A graph theoretic approach to ultrafast information distribution: borel Cayley graph resizing algorithm,” Computer Communications, vol. 33, no. 17, pp. 2093–2104, 2010. View at Publisher · View at Google Scholar · View at Scopus
  28. J. W. Mao and C. B. Yang, “Shortest path routing and fault-tolerant routing on de Bruijn networks,” Networks, vol. 35, no. 3, pp. 207–215, 2000. View at Scopus
  29. C. T. Ho and L. Stockmeyer, “A new approach to fault-tolerant wormhole routing for mesh-connected parallel computers,” IEEE Transactions on Computers, vol. 53, no. 4, pp. 427–438, 2004. View at Publisher · View at Google Scholar · View at Scopus
  30. R. V. Boppana and S. Chalasani, “Fault-tolerant wormhole routing algorithms for mesh networks,” IEEE Transactions on Computers, vol. 44, no. 7, pp. 848–864, 1995. View at Publisher · View at Google Scholar · View at Scopus
  31. C. Intanagonwiwat, R. Govindan, D. Estrin, J. Heidemann, and F. Silva, “Directed diffusion for wireless sensor networking,” IEEE/ACM Transactions on Networking, vol. 11, no. 1, pp. 2–16, 2003. View at Publisher · View at Google Scholar · View at Scopus
  32. B. Parhami, Introduction to Parallel Processing: Algorithms and Architectures, Kluwer Academic, Norwell, Mass, USA, 1999.
  33. Z. Feng and O. W. Yang, “Routing algorithms in the bidirectional de Bruijn graph metropolitan area networks,” in Proceedings of the Military Communications Conference (MILCOM '94), vol. 3, pp. 957–961, IEEE, October 1994. View at Scopus
  34. E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische Mathematik, vol. 1, no. 1, pp. 269–271, 1959. View at Publisher · View at Google Scholar · View at Scopus