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Hop-Constrained Oblivious Routing Using Prim’s-Sollin’s Algorithm

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Advanced Information Networking and Applications (AINA 2024)

Part of the book series: Lecture Notes on Data Engineering and Communications Technologies ((LNDECT,volume 204))

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Abstract

Our objective is to optimize routing efficiency and scalability within extensive networks through the development of streamlined oblivious routing methods, ensuring optimal load balancing and the utilization of compact routing tables. This initiative aims to enhance overall routing efficiency, reduce source demands, and elevate network reliability and availability. Addressing the challenge of implementing hop-constrained oblivious routing within near-linear time represents a pivotal step in advancing network routing capabilities, mitigating congestion, and minimizing path lengths.

The open problem of constructing hop-constrained oblivious routing in \(O(m^{1+O(1)})\) time provides an opportunity for innovative solutions [12]. This challenge is effectively tackled through the application of Prim’s-Sollin’s algorithm, resulting in a time complexity approaching linearity while maintaining minimal congestion and dilation. The algorithm, rooted in the principles of finding the smallest spanning tree in a graph, adheres to specified hop limitations and preserves the shortest distance between hops. Hop- constrained oblivious routing, when implemented with Prim’s-Sollin’s algorithm, demonstrates a commendable time complexity of O(mloglogn), underscoring its remarkable efficiency and effectiveness in large-scale network environments.

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References

  1. ICS 161. Design and analysis of algorithms lecture notes for 6 February 1996 (Year Published/ Last Updated). https://ics.uci.edu/~eppstein/161/960206.html

  2. Amir, D., Wilson, T., Shrivastav, V., Weatherspoon, H., Kleinberg, R., Agarwal, R.: Optimal oblivious reconfigurable networks. In: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, pp. 1339–1352 (2022)

    Google Scholar 

  3. Applegate, D., Cohen, E.: Making intra-domain routing robust to changing and uncertain traffic demands: understanding fundamental tradeoffs. In: Proceedings of the 2003 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications, pp. 313–324 (2003)

    Google Scholar 

  4. Aspnes, J., et al.: Eight open problems in distributed computing. Bull. EATCS 90, 109–126 (2006)

    Google Scholar 

  5. Azar, Y., Cohen, E., Fiat, A., Kaplan, H., Racke, H.: Optimal oblivious routing in polynomial time. In: Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, pp. 383–388 (2003)

    Google Scholar 

  6. Bienkowski, M., Korzeniowski, M., Räcke, H.: A practical algorithm for constructing oblivious routing schemes. In: Proceedings of the Fifteenth Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 24–33 (2003)

    Google Scholar 

  7. Busch, C., Magdon-Ismail, M.: Optimal oblivious routing in hole-free networks. In: Zhang, X., Qiao, D. (eds.) Quality, Reliability, Security and Robustness in Heterogeneous Networks, pp. 421–437. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29222-4_30

  8. Busch, C., Magdon-Ismail, M., Xi, J.: Oblivious routing on geometric networks. In: Proceedings of the Seventeenth Annual ACM Symposium on Parallelism in Algorithms and Architectures, pp. 316–324 (2005)

    Google Scholar 

  9. Busch, C., Magdon-Ismail, M., Xi, J.: Optimal oblivious path selection on the mesh. IEEE Trans. Comput. 57(5), 660–671 (2008)

    Article  MathSciNet  Google Scholar 

  10. Fakcharoenphol, J., Rao, S., Talwar, K.: A tight bound on approximating arbitrary metrics by tree metrics. In: Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, pp. 448–455 (2003)

    Google Scholar 

  11. Gabow, H.N., Galil, Z., Spencer, T., Tarjan, R.E.: Efficient algorithms for finding minimum spanning trees in undirected and directed graphs. Combinatorica 6(2), 109–122 (1986)

    Article  MathSciNet  Google Scholar 

  12. Ghaffari, M., Haeupler, B., Zuzic, G.: Hop-constrained oblivious routing. In: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, pp. 1208–1220 (2021)

    Google Scholar 

  13. Gupta, A., Hajiaghayi, M.T., Räcke, H.: Oblivious network design. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm, pp. 970–979 (2006)

    Google Scholar 

  14. Hajiaghayi, M.T., Kleinberg, R.D., Leighton, T., Räcke, H.: New lower bounds for oblivious routing in undirected graphs. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm, pp. 918–927. Citeseer (2006)

    Google Scholar 

  15. Hao, F., Kodialam, M., Lakshman, T.: Hop constrained maximum flow with segment routing, US Patent 10,374,939 (2019)

    Google Scholar 

  16. Harrelson, C., Hildrum, K., Rao, S.: A polynomial-time tree decomposition to minimize congestion. In: Proceedings of the Fifteenth Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 34–43 (2003)

    Google Scholar 

  17. Harsha, P., Hayes, T.P., Narayanan, H., Räcke, H., Radhakrishnan, J.: Minimizing average latency in oblivious routing. In: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 200–207 (2008)

    Google Scholar 

  18. Karger, D.R., Klein, P.N., Tarjan, R.E.: A randomized linear-time algorithm to find minimum spanning trees. J. ACM 42(2), 321–328 (1995)

    Article  MathSciNet  Google Scholar 

  19. Leighton, F.T., Maggs, B.M., Rao, S.B.: Packet routing and job-shop scheduling in o (congestion+ dilation) steps. Combinatorica 14(2), 167–186 (1994)

    Article  MathSciNet  Google Scholar 

  20. Maggs, B.M., auf der Heide, F.M., Vocking, B., Westermann, M.: Exploiting locality for data management in systems of limited bandwidth. In: Proceedings 38th Annual Symposium on Foundations of Computer Science, pp. 284–293. IEEE (1997)

    Google Scholar 

  21. Marpaung, F., et al.: Comparative of prim’s and Boruvka’s algorithm to solve minimum spanning tree problems. J. Phys.: Conf. Ser. 1462, 012043 (2020). IOP Publishing

    Google Scholar 

  22. Németh, G.: On the competitiveness of oblivious routing: a statistical view. Appl. Sci. 11(20), 9408 (2021)

    Article  Google Scholar 

  23. Rabin, M.O.: Efficient dispersal of information for security, load balancing, and fault tolerance. J. ACM 36(2), 335–348 (1989)

    Article  MathSciNet  Google Scholar 

  24. Racke, H.: Minimizing congestion in general networks. In: Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002, pp. 43–52. IEEE (2002)

    Google Scholar 

  25. Räcke, H.: Optimal hierarchical decompositions for congestion minimization in networks. In: Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing, pp. 255–264 (2008)

    Google Scholar 

  26. Räcke, H.: Survey on oblivious routing srtategies. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds.) Mathematical Theory and Computational Practice, pp. 419–429. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03073-4_43

  27. Räcke, H., Schmid, S.: Compact oblivious routing. arXiv preprint arXiv:1812.09887 (2018)

  28. Scheideler, C.: Universal Routing Strategies for Interconnection Networks. Springer, Heidelberg (1998)

    Google Scholar 

  29. Srinivasan, A., Teo, C.P.: A constant-factor approximation algorithm for packet routing, and balancing local vs. global criteria. In: Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pp. 636–643 (1997)

    Google Scholar 

  30. Upfal, E.: Efficient schemes for parallel communication. J. ACM 31(3), 507–517 (1984)

    Article  MathSciNet  Google Scholar 

  31. Valiant, L.G., Brebner, G.J.: Universal schemes for parallel communication. In: Proceedings of the Thirteenth Annual ACM Symposium on Theory of Computing, pp. 263–277 (1981)

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Engineering, National Institute of Technology, Hamirpur, Hamirpur, Himachal Pradesh, 177 005, India

    Mehak & Dharmendra Prasad Mahato

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  1. Mehak
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  2. Dharmendra Prasad Mahato
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Correspondence to Mehak .

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  1. Department of Information and Communication Engineering, Fukuoka Institute of Technology, Fukuoka, Japan

    Leonard Barolli

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Mehak, Mahato, D.P. (2024). Hop-Constrained Oblivious Routing Using Prim’s-Sollin’s Algorithm. In: Barolli, L. (eds) Advanced Information Networking and Applications. AINA 2024. Lecture Notes on Data Engineering and Communications Technologies, vol 204. Springer, Cham. https://doi.org/10.1007/978-3-031-57942-4_43

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