Space-Stretch Tradeoff Optimization for Routing in Internet-Like Graphs

  • Tang, Mingdong (Schoool of Computer Science and Engineering, Hunan University of Science and Technology) ;
  • Zhang, Guoqiang (School of Computer Science and Technology, Nanjing Normal University) ;
  • Liu, Jianxun (Schoool of Computer Science and Engineering, Hunan University of Science and Technology)
  • Received : 2011.10.07
  • Accepted : 2012.06.28
  • Published : 2012.10.31

Abstract

Compact routing intends to achieve good tradeoff between the routing path length and the memory overhead, and is recently considered as a main alternative to overcome the fundamental scaling problems of the Internet routing system. Plenty of studies have been conducted on compact routing, and quite a few universal compact routing schemes have been designed for arbitrary network topologies. However, it is generally believed that specialized compact routing schemes for peculiar network topologies can have better performance than universal ones. Studies on complex networks have uncovered that most real-world networks exhibit power-law degree distributions, i.e., a few nodes have very high degrees while many other nodes have low degrees. High-degree nodes play the crucial role of hubs in communication and inter-networking. Based on this fact, we propose two highest-degree landmark based compact routing schemes, namely HDLR and $HDLR^+$. Theoretical analysis on random power-law graphs shows that the two schemes can achieve better space-stretch trade-offs than previous compact routing schemes. Simulations conducted on random power-law graphs and real-world AS-level Internet graph validate the effectiveness of our schemes.

Keywords

References

  1. L. Cowen, "Compact routing with minimum stretch," J. Algorithms, vol. 38, no. 1, pp. 170-183, 2001. https://doi.org/10.1006/jagm.2000.1134
  2. M. Thorup and U. Zwick, "Compact routing schemes," in Proc. SPAA, 2001, pp. 1-10.
  3. C. Gavoille and M.Gengler, "Space-Efficiency for routing schemes of stretch factor three," J. Parallel Distrib. Comput., vol. 61, no. 5, pp. 679-687, 2001. https://doi.org/10.1006/jpdc.2000.1705
  4. P. Fraigniaud and C. Gavoille, "Routing in trees," in Proc. ICALP, 2001, pp. 757-772.
  5. K. A. Laing, "Name-independent compact routing in trees," Inf. Process. Lett., vol. 103, no. 2, pp. 57-60, 2007. https://doi.org/10.1016/j.ipl.2007.02.015
  6. H. Lu, "Improved compact routing tables for planar networks via orderly spanning trees," in Proc. COCOON, 2002, pp. 57-66.
  7. I. Abraham and D. Malkhi,"Name independent routing for growth bounded networks," in Proc. SPAA, 2005, pp. 49-55.
  8. G. Konjevod, A. Richa, and D. Xia, "Optimal scale-free compact routing schemes in networks of low doubling dimension," in Proc. ACM-SIAM SODA, 2007, pp. 939-948.
  9. I. Abraham, C. Gavoille, A. V. Goldberg, and D.Malkhi, "Routing in networks with low doubling dimension," in Proc. ICDCS, 2006.
  10. M. Faloutsos, P. Faloutsos, and C. Faloutsos, "On power-law relationships of the Internet topology," Comput. Commun. Rev., vol. 29, pp. 251-262, 1999. https://doi.org/10.1145/316194.316229
  11. G. Q. Zhang, B. Quoitin, and S. Zhou, "Phase changes in the evolution of the IPv4 and IPv6 AS-level Internet topologies," Comput. Commun., vol. 34, pp. 649-657, 2011. https://doi.org/10.1016/j.comcom.2010.06.004
  12. M. Ripeanu, A. Iarmnitchi, and I. Foster, "Mapping the Gnutella network," IEEE Internet Comput., pp. 50-57, Jan. 2002.
  13. R. Albert, H. Jeong, and A. L. Barabasi, "Diameter of the world wide web," Nature, vol. 401, pp. 130-131, 1999. https://doi.org/10.1038/43601
  14. D. Krioukov, K. Fall, and X.Yang, "Compact routing on Internet-like graphs," in Proc. IEEE INFOCOM, 2004, pp. 209-219.
  15. A. Brady and L. Cowen, "Compact routing on power law graphs with additive stretch," in Proc. ALENEX, 2006, pp. 119-128.
  16. S. Carmi, R. Cohen, and D. Dolev, "Searching complex networks efficiently with minimal information," Europhysics Lett., vol. 74, pp. 1102-1108, 2006. https://doi.org/10.1209/epl/i2006-10049-1
  17. M. Enachescu, M. Wang, and A. Goel, "Reducing maximum stretch in compact routing," in Proc. IEEE INFOCOM, 2008, pp. 977-985.
  18. I. Norros, "Powernet: Compact routing on Internet-like random networks," in Proc. NGI, Aveiro, 2009.
  19. D. Meyer, L. Zhang, and K. Fall, "Report from the IAB workshop on routing and addressing," The Internet Architecture Board, 2007.
  20. G. Huston. (2001. Mar.). Analyzing the Internet's BGP routing table. Internet Protocol J. 4(1). [Online]. Available: http://www.cisco.com/web/about/ac123/ac147/archived-issues/ipj-4-1/bgp-routing-table.html
  21. D. Krioukov and K. Claffy, "On compact routing for the Internet," ACM SIGCOMM Comput. Commun. Rev., vol. 37, no. 3, pp.43-52, 2007. https://doi.org/10.1145/1198255.1198262
  22. F. Chung and L. Lu, "The average distances in random graphs with given expected degrees," in Proc. National Academy Sci., vol. 99, 2002, pp. 15879-15882. https://doi.org/10.1073/pnas.252631999
  23. L. Lu, "Probabilistic methods in massive graphs and Internet computing," University of California San Diego, 2002.
  24. T. Eilam, C. Gavoille, and D. Peleg, "Compact routing schemes with low stretch factor," in Proc. ACM PODC, Puerto Vallarta, Mexico, 1998, pp. 11-20.
  25. M. Thorup and U. Zwick, "Approximate distance oracles," in Proc. ASM STOC, 2001.
  26. A. Barabasi and R. Albert, "Emergence of scaling in random network," Science, vol. 286, pp. 509-512, 1999. https://doi.org/10.1126/science.286.5439.509
  27. G. Q. Zhang, G. Q. Zhang, Q. F. Yang, S. Q. Cheng, and T. Zhou. (2008, Dec.). Evolution of the Internet and its cores. New J. Phys. [Online]. 10(12). Available: http://iopscience.iop.org/1367-2630/10/12/123027
  28. CAIDA's Skitter project. CAIDA. [Online]. Available: http://www.caida. org/tools/measurement/skitter/
  29. W. Chen, C. Sommer, S. H. Teng, and Y. Wang, "Compacting routing in power-law graphs," in Proc. DISC, Sept. 2009.
  30. I. Norros and H. Reittu, "Network models with a 'soft hierarchy': A random graph construction with loglog scalability," IEEE Netw., vol.22, no. 2, pp. 40-46, 2008. https://doi.org/10.1109/MNET.2008.4476070
  31. S. Zhou and R. J. Mondragon, "The rich-club phenomenon in the Internet topology," IEEE Commun. Lett., vol. 3, pp. 180-182, 2004.