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Advancements in Routing Theory: Applications, Challenges, and Future Directions

This report outlines significant progress in routing theory, emphasizing its applications to realistic network topologies and exploring future directions for research. Key topics include the trade-offs between adaptation costs, memory space, and path length stretch. While recent breakthroughs have improved routing efficiency, challenges remain in dynamic environments. The proposal to NSF suggests the development of mathematically rigorous next-generation routing protocols. Collaborative efforts on Internet topology analysis and modeling are underway, aiming to harness real data for enhanced routing solutions.

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Advancements in Routing Theory: Applications, Challenges, and Future Directions

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  1. RR-FS Status Report Dmitri Krioukov CAIDA dima@caida.org IETF-60

  2. Outline • Progress in routing theory • Applications to realistic topologies • Future directions • Recent advances

  3. Outline • Progress in routing theory • Applications to realistic topologies • Future directions • Recent advances

  4. Inevitable trade-offs Triangle of trade-offs: • Adaptation costs = convergence measures (e.g. number of messages per topology change) • Memory space = routing table size • Stretch = path length inflation

  5. What’s known • No recent progress on the dynamic case (adaptations costs are excluded) • Lower bound (n/s) • Graph theory is a static theory • Memory vs. stretch • Shortest path (s=1)  (n log n) • 1  s < 1.4  (n log n) • 1.4  s < 3  (n) • 3  s < 5  (n1/2)

  6. Recent “very static” breakthroughs • L. Cowen. Compact routing with minimum stretch. Symposium on Discrete Algorithms (SODA) 1999. • s=3, ~O(n2/3) • M. Thorup and U. Zwick. Compact routing schemes. Symposium on Parallel Algorithms and Architectures (SPAA)2001. • s=3, ~O(n1/2) • On trees: s=1, ~O(1) ( = (1+o(1)) log n) • All forwarding decisions are O(1) time

  7. Recent “less static” breakthroughs:name-independence • M. Arias, et al. Compact routing with name independence. SPAA 2003. • s=5, ~O(n1/2) • I. Abraham, et al. Compact name-independent routing with minimum stretch. SPAA 2004. • s=3, ~O(n1/2)

  8. Outline • Progress in routing theory • Applications to realistic topologies • Future directions • Recent advances

  9. Compact routing onInternet-like graphs • D. Krioukov, et al. Compact routing on Internet-like graphs. INFOCOM 2004. • Average stretch of the TZ scheme on power-law graphs: • is low (~1.1, ~70% paths are shortest) • does not depend on  • decreases with n • Routing table size is well below its upper bounds (52 vs. 2,187 for n=10,000) • The average stretch function has a unique critical point and the Internet is located in its close neighborhood… (which is quite surprising)

  10. Outline • Progress in routing theory • Applications to realistic topologies • Future directions • Recent advances

  11. Proposal to NSF Title: Toward mathematically rigorous next-generation routing protocols on realistic network topologies; agenda: • Routing: • Name-independent routing on realistic graphs • Low average stretch routing on realistic graphs • Topology (what are realistic graphs) • Traceroute-based AS-level topology data • Comparative analysis of Internet topologies obtained from different data sources • Modeling of the Internet topology evolution • Graph entropy-based extensions to existing methodologies

  12. Outline • Progress in routing theory • Applications to realistic topologies • Future directions • Recent advances

  13. Work just started • Comparative analysis of Internet topologies (with P. Mahadevan, UCSD) • Internet topology evolution modeling (with R. Liu, UCLA)

  14. Recent results • Inference of business relationships between ASs (w/ X. Dimitropoulos, Georgia Tech) • Why relevant • Routing  • Topology  • Modeling  • Validation (real data)

  15. AS relationship inference • Node-degree based approach • produces many paths inconsistent with standard BGP import-export policies (invalid paths) • Invalid path minimization approach • produces unrealistic AS hierarchies • Our approach • uses multiobjective optimization of the two objective functions above • casts the problem as a semidefinite programming relaxation of MAX2SAT • resolves the issues associated with both approaches

  16. Last slide • Homepage http://rr-fs.caida.org/ will be updated soon (will send email to the list) • Mailing list subscriptions requests, collaboration proposals, questions, comments, etc: dima@caida.org • Thank you

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