Abstract
With the fast development of Internet, the size of routing table in the backbone router continues to grow rapidly. forwarding information base (FIB), which is derived from routing table, is stored in line-card to conduct routing lookup. Since the line-card’s memory is limited, it would be worthwhile to compress the FIB for consuming less storage. Therefore, various FIB compression algorithms have been proposed. However, there is no well-presented mathematical support for the feasibility of the FIB compression solution, nor any mathematical derivation to prove the correctness of these algorithms. To address these problems, we propose a universal mathematical method based on the Group theory. By defining a Group representing the longest prefix matching rule, the bound of the worst case of FIB compression solution can be figured out. Furthermore, in order to guarantee the ultimate correctness of FIB compression algorithms, routing table equation test is proposed and implemented to verify the equivalence of the two routing tables before and after compression by traversing the 32-bit IP address space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Trie is a tree-based data structure allowing the organization of prefixes on a digital basis by using the bits of prefixes to direct the branching (Ruiz-Sánchez et al. 2001).
Both FIB compression and overlap elimination algorithms transform the binary trie, thus they are called trie-transformation algorithms in this paper.
Group (mathematics) (Vvedensky 2005) is a set together with a binary operation satisfying certain algebraic conditions.
FIB is also known as forwarding table, which is stored in line-cards to forward data packets. Each entry of FIB stores a prefix and the corresponding next-hop, such as 200.45.65.0/24:40. It suggests that if an incoming IP address matched the prefix 200.45.65.0/24 by LPM, this packet should be forwarded to the interface 40 (40 is also related to a corresponding next-hop IP address).
In this paper, Full IP Address Space refers to the binary trie whose internal nodes are all pushed to level 32.
References
Brualdi, R.A.: Introductory Combinatorics, Chapter 3, 5th edn, pp. 69–70. Machine Press China, Beijing (2009)
Cain, B.: Auto aggregation method for IP prefix/length pairs. http://www.patentgenius.com/patent/6401130.html (2002)
Dai, H., Zhong, Y., Liu, A.X., Wang, W., Li, M.: Noisy bloom filters for multi-set membership testing. In: Proc. ACM SIGMETRICS, pp 139–151 (2016)
Dai, H., Shahzad, M., Liu, A.X., Zhong, Y.: Finding persistent items in data streams. Proc. VLDB Endow. 10(4), 289–300 (2016)
Dai, H., Meng, L., Liu, A.X.: Finding persistent items in distributed, datasets. In: Proc. IEEE INFOCOM (2018)
Degermaerk, M., Brodnik, A., Carlsson, S., and Pink, S: Small forwarding tables for fast routing lookups. In: Proc. SIGCOMM, NY (1997)
Draves, R., King, C., Venkatachary, S., Zill, B.D.: Constructing optimal IP routing tables. In: Proc. IEEE INFOCOM, pp. 88–97 (1999)
IETF Global Routing Operations (GROW). http://datatracker.ietf.org/wg/grow/charter/ (2015)
IRTF Routing Research Group. https://irtf.org/concluded/rrg (2014)
Korosi, A., Tapolcai, J., Mihálka, B., Mészáros, G., Rétvári, G.: Compressing IP forwarding tables: realizing information-theoretical space bounds and fast lookups simultaneously. In: Proc. IEEE ICNP, IEEE, pp. 332–343 (2014)
Li, D., Cui, H., Hu, Y., et al.: Scalable data center multicast using multi-class bloom filter, network protocols (ICNP). In: 19th IEEE international conference on, pp. 266–275 (2011)
Li, Q., Wang, D., Xu, M., Yang, J.: On the scalability of router forwarding tables: nexthop-selectable FIB aggregation. In: Proc. IEEE INFOCOM (2011)
Li, Q., Xu, M., Chen, M.: NSFIB construction and aggregation with next hop of strict partial order. INFOCOM, 2013, pp. 550–554. In: Proceedings IEEE. IEEE (2013)
Li, F.Z., Xiao, S.W., Pei, T., Li, Jie: Achievable rate maximization for cognitive hybrid satellite-terrestrial networks with af-relays. IEEE J. Sel. Areas Commun. 36(2), 304–313 (2018)
Li, Z., Chang, B., Wang, S., Liu, A., Zeng, F, Luo, G.: Dynamic compressive wide-band spectrum sensing based on channel energy reconstruction in cognitive internet of things. IEEE Trans. Ind. Inf. (2018)
Lin, D., Zhang, Y., Hu, C., Liu, B., Zhang, X., Pao, D.: Route table partitioning and load balancing for parallel searching with TCAMs. In: Proc. IPDPS (2007)
Liu, Y., Zhao, X., Nam, K., Wang, L., Zhang, B.: Incremental forwarding table aggregation. In: Proc. IEEEE GLOBECOM (2010)
Meng, X., Xu, Z., Zhang, B., Huston, G., Lu, S., Zhang, L.: IPv4 address allocation and the BGP routing table. ACM SIGCOMM Comput Commun Rev 35, 71–80 (2005)
Nilsson, S., Karlsson, G.: Fast address look-up for internet routers. In: Proceedings of IEEE broadband communications (1998)
Rétvári, G., Tapolcai, J., Kőrösi, A., Majdán, A., Heszberger, Z.: Compressing IP forwarding tables: towards entropy bounds and beyond. ACM SIGCOMM Comput. Commun. Rev. 43, 111–122 (2013)
RIPE Network Coordination Centre. http://www.ripe.net/data-tools/stats/ris/ris-raw-data
Rottenstreich, O., Radan, M., Cassuto, Y., Keslassy, I., Arad, C., Mizrahi, T., Revah, Y., Hassidim, A.: Compressing forwarding tables. In: Proc. IEEE INFOCOM, IEEE, pp. 1231–1239 (2013)
Ruiz-Sánchez, M.Á., Biersack, E.W., Dabbous, W.: Survey and taxonomy of IP address lookup algorithms. Netw. IEEE 15, 8–23 (2001)
Srinivasan, V., Varghese, G.: Fast IP lookups using controlled prefix expansion. ACM TOCS 17, 1–40 (1999)
Vvedensky, D.D.: Group Theory, pp. 14–15. World Scientific Pub., Singapore (2005)
Waldvogel, M., Varghese, G., Turner, J., Plattner, B.: Scalable high speed ip routing lookups. ACM. 27(4), 25–36 (1997)
Xiao, F., Wang, Z., Ye, N., Wang, R., Li, X.-Y.: One more tag enables fine-grained RFID localization and tracking. IEEE/ACM Trans. Netw. 26(1), 161–174 (2018a)
Xiao, F., Chen, L., Sha, C., Sun, L., Wang, R., Liu, A.X., Ahmed, F.: Noise tolerant localization for sensor networks. IEEE/ACM Trans. Netw. 26(4), 1701–1704 (2018b)
Yang, T., Duan, R., Lu, J., Zhang, S., Dai, H., Liu, B.: CLUE: achieving fast update over compressed table for parallel lookup with reduced dynamic redundancy. In: Proc. IEEE ICDCS (2012)
Yang, T., Zhang, T., Zhang, S., Liu, B.: Constructing optimal non-overlap routing tables. Accepted by Proc. IEEE ICC (2012)
Yu, H.: A memory- and time-efficient on-chip TCAM minimizer for IP lookup. DATE ‘10. In: Proceedings of the conference on design, automation and test in Europe (2010)
Zhao, X., Liu, Y., Wang, L., Zhang, B.: On the aggregatability of router forwarding tables. In: Proc. IEEE INFOCOM (2010)
Zheng, K., Hu, C., Lu, H., Liu, B.: A TCAM-based distributed parallel IP lookup scheme and performance analysis. IEEE/ACM Trans. Netw. 14, 863–875 (2006)
Zhu, H., Xiao, F., Lijuan, S., Wang, R., Yang, P.: R-TTWD: robust device-free through-the-wall detection of moving Human with WiFi. IEEE J. Sel. Areas Commun. 35(5), 1090–1103 (2017)
Acknowledgements
We would like to thank the anonymous reviewers for their thoughtful suggestions. This work is partially supported by Primary Research & Development Plan of China (2018YFB1004403), National Basic Research Program of China (973 Program, 2014CB340405), and NSFC (61672061).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
Additional information
Co-primary authors: Tong Yang and Jinyang Li.
Rights and permissions
About this article
Cite this article
Yang, T., Li, J., Zhao, C. et al. Mathematical analysis on forwarding information base compression. CCF Trans. Netw. 1, 16–27 (2019). https://doi.org/10.1007/s42045-018-0010-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42045-018-0010-1