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Two-Dimensional Packet Classification and Filter Conflict Resolution in the Internet

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Abstract

In this paper, we study the packet classification problem and the filter conflict resolution problem, both motivated by applications in the routing of packets in an IP network. For the first problem, we focus on the static 2-dimensional conflict-free (i.e., nested) filters. We design a linear space data structure with O(T w (n)+(log log n)2) query time on a RAM with word size O(w) bits where n is the number of filters in the router, w is the number of bits in an IP address and

$$T_{w}(n)=O\biggl(\min\biggl\{\log w,\frac{\log w\log\log n}{\log\log w},\sqrt{\frac{\log n}{\log\log n}}\biggr\}\biggr).$$

This is the first optimal space data structure with poly-logarithmic query time for this problem.

In practice, network filters often contain very few conflicts but are not completely conflict-free. Fortunately, conflicts can be resolved by adding conflict-resolving filters. Moreover, practical filters often possess another slightly different nesting property which we called 1-nestedness. We present an algorithm to resolve conflicts in a set of 1-nested filters in O(nT w (n)+k) time and linear space, where k is the number of filter pairs in conflict. Furthermore, we show that our data structure for the first problem can be adapted to apply on conflict-resolved 1-nested filters with the same query and space complexities.

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References

  1. Adiseshu, H., Suri, S., Garulkar, G.: Detecting and resolving packet filter conflicts. In: Proceedings of the 19th Annual Joint Conference of the IEEE Computer and Communications Societies, pp. 1203–1212. IEEE, Tel Aviv (2000)

    Google Scholar 

  2. Andersson, A.: Faster deterministic sorting and searching in linear space. In: Proceedings of the 37th Annual Symposium on Foundations of Computer Science, pp. 135–141. IEEE, Burlington (1996)

    Google Scholar 

  3. Andersson, A., Thorup, M.: Tight(er) worst-case bounds on dynamic searching and priority queues. In: Proceedings of the 32th Annual ACM Symposium on Theory of Computing, pp. 335–342. ACM, Portland (2000)

    Google Scholar 

  4. Baboescu, F., Varghese, G.: Scalable packet classification. In: Proceedings of the 2001 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, pp. 199–210. ACM, San Diego (2001)

    Chapter  Google Scholar 

  5. Beame, P., Fich, F.: Optimal bounds for the predecessor problem and related problems. J. Comput. Syst. Sci. 65(1), 38–73 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Buddhikot, M., Suri, S., Waldvogel, M.: Space decomposition techniques for fast Layer-4 switching. In: Proceedings of IFIP Workshop on Protocols for High Speed Networks, pp. 25–41. Kluwer, Salem (1999)

    Google Scholar 

  7. Dietz, P.F.: Fully persistent arrays. In: Workshop on Algorithms and Data Structures. Lecture Notes in Computer Science, vol. 382, pp. 67–74. Springer, Berlin (1989)

    Google Scholar 

  8. Dietzfelbinger, M., Karlin, A., Melhorn, M., Meyer auf der Heide, F., Rohnert, H., Tarjan, R.E.: Dynamic perfect hashing: upper and lower bounds. SIAM J. Comput. 23(4), 738–761 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  9. Driscoll, J.R., Sarnak, N., Sleator, D.D., Tarjan, R.E.: Making data structures persistent. J. Comput. Syst. Sci. 38, 86–124 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  10. Eppstein, D., Muthukrishnan, S.: Internet packet filter management and rectangle geometry. In: Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 827–835. SIAM, Washington (2001)

    Google Scholar 

  11. Feldman, A., Muthukrishnan, S.: Tradeoffs for packet classification. In: Proceedings of the 19th Annual Joint Conference of the IEEE Computer and Communications Societies, pp. 1193–1202. IEEE, Tel Aviv (2000)

    Google Scholar 

  12. Gupta, P., McKeown, N.: Packet classification on multiple fields. In: Proceedings of the 1999 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, pp. 147–160. ACM, Cambridge (1999)

    Chapter  Google Scholar 

  13. Gupta, P., McKeown, N.: Classifying packets with hierarchical intelligent cuttings. IEEE Micro 20(1), 34–41 (2000)

    Article  Google Scholar 

  14. Gupta, P., McKeown, N.: Dynamic algorithms with worst-case performance for packet classification. In: IFIP Networking 2000. Lecture Notes in Computer Science, vol. 1815, pp. 528–539. Springer, Paris (2000)

    Google Scholar 

  15. Kaplan, H., Molad, E., Tarjan, R.E.: Dynamic rectangular intersection with priorities. In: Proceedings of the 35th Annual ACM Symposium on Theory of Computing, pp. 639–648. ACM, San Diego (2003)

    Google Scholar 

  16. Lakshman, T.V., Stiliadis, D.: High-speed policy-based packet forwarding using efficient multi-dimensional range matching. In: Proceedings of the 1998 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, pp. 203–214. ACM, Vancouver (1998)

    Chapter  Google Scholar 

  17. Sarnak, N., Tarjan, R.E.: Planar point location using persistent search trees. Commun. ACM. 29(7), 669–679 (1986)

    Article  MathSciNet  Google Scholar 

  18. Srinivasan, V.: A packet classification and filter management system. In: Proceedings of the 20th Annual Joint Conference of the IEEE Computer and Communications Societies, pp. 1464–1473. IEEE, Anchorage (2001)

    Google Scholar 

  19. Srinivasan, V., Suri, S., Varghese, G.: Packet classification using tuple space search. In: Proceedings of the 1999 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, pp. 135–146. ACM, Cambridge (1999)

    Chapter  Google Scholar 

  20. Srinivasan, V., Varghese, G., Suri, S., Waldvogel, M.: Fast and scalable layer four switching. In: Proceedings of the 1998 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, pp. 191–202. ACM, Vancouver (1998)

    Chapter  Google Scholar 

  21. Thorup, M.: Space efficient dynamic stabbing with fast queries. In: Proceedings of the Thirty Fifth Annual ACM Symposium on Theory of Computing, pp. 649–658. ACM, New York (2003)

    Chapter  Google Scholar 

  22. Van Emde Boas, P.: Preserving order in a forest in less than logarithmic time. In: Proceedings of the 16th Annual Symposium on Foundations of Computer Science, pp. 75–84. IEEE, Berkeley (1975)

    Google Scholar 

  23. Waldvogel, M., Varghese, G., Turner, J., Plattner, B.: Scalable high speed IP routing lookups. In: Proceedings of the 1997 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, pp. 25–36. ACM, Cannes (1997)

    Chapter  Google Scholar 

  24. Warkhede, P., Suri, S., Varghese, G.: Fast packet classification for two-dimensional conflict-free filters. In: Proceedings of the 20th Annual Joint Conference of the IEEE Computer and Communications Societies, pp. 1434–1443. IEEE, Anchorage (2001)

    Google Scholar 

  25. Willard, D.E.: Log-logarithmic worst-case range queries are possible in space θ(n). Inform. Process. Lett. 17(2), 81–84 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  26. Woo, T.Y.C.: A modular approach to packet classification: algorithms and results. In: Proceedings of the 19th Annual Joint Conference of the IEEE Computer and Communications Societies, pp. 1213–1222. IEEE, Tel Aviv (2000)

    Google Scholar 

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Correspondence to Chung Keung Poon.

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This research was fully supported by a grant from the Research Grants Council of the Hong Kong SAR, China (City U 1164/04E). A preliminary version appeared in ISPAN’04.

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Kwok, A., Poon, C.K. Two-Dimensional Packet Classification and Filter Conflict Resolution in the Internet. Theory Comput Syst 44, 289–303 (2009). https://doi.org/10.1007/s00224-007-9050-5

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