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Multi-commodity Flow with In-Network Processing

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Algorithmic Aspects of Cloud Computing (ALGOCLOUD 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11409))

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Abstract

Modern networks run “middleboxes” that offer services ranging from network address translation and server load balancing to firewalls, encryption, and compression. In an industry trend known as Network Functions Virtualization (NFV), these middleboxes run as virtual machines on any commodity server, and the switches steer traffic through the relevant chain of services. Network administrators must decide how many middleboxes to run, where to place them, and how to direct traffic through them, based on the traffic load and the server and network capacity. Rather than placing specific kinds of middleboxes on each processing node, we argue that server virtualization allows each server node to host all middlebox functions, and simply vary the fraction of resources devoted to each one. This extra flexibility fundamentally changes the optimization problem the network administrators must solve to a new kind of multi-commodity flow problem, where the traffic flows consume bandwidth on the links as well as processing resources on the nodes. We show that allocating resources to maximize the processed flow can be optimized exactly via a linear programming formulation, and to arbitrary accuracy via an efficient combinatorial algorithm. Our experiments with real traffic and topologies show that a joint optimization of node and link resources leads to an efficient use of bandwidth and processing capacity. We also study a class of design problems that decide where to provide node capacity to best process and route a given set of demands, and demonstrate both approximation algorithms and hardness results for these problems.

Y. Naamad—This work was done while the author was at the Department of Computer Science, Princeton University.

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Notes

  1. 1.

    To be precise, this paper shows the aforementioned hardness for Max Cut. A simple approximation preserving reduction from Max Cut to Max Bisection can be derived by looking at maximum cuts of the graph formed by 2 disjoint copies of the Max Cut instance graph.

References

  1. Anwer, B., Benson, T., Feamster, N., Levin, D.: Programming Slick network functions. In: Proceedings of Symposium on SDN Research, June 2015

    Google Scholar 

  2. Arora, S., Hazan, E., Kale, S.: The multiplicative weights update method: a meta-algorithm and applications. Theor. Comput. 8(1), 121–164 (2012)

    Article  MathSciNet  Google Scholar 

  3. Berman, P., Karpinski, M.: On some tighter inapproximability results (extended abstract). In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 200–209. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48523-6_17

    Chapter  Google Scholar 

  4. Chakrabarty, D., Krishnaswamy, R., Li, S., Narayanan, S.: Capacitated network design on undirected graphs. In: Raghavendra, P., Raskhodnikova, S., Jansen, K., Rolim, J.D.P. (eds.) APPROX/RANDOM -2013. LNCS, vol. 8096, pp. 71–80. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40328-6_6

    Chapter  Google Scholar 

  5. Chiosi, M., et al.: Network functions virtualisation: introductory white paper. In: SDN and OpenFlow World Congress, October 2012

    Google Scholar 

  6. Cohen, R., Lewin-Eytan, L., Naor, J.S., Raz, D.: Near optimal placement of virtual network functions. In: IEEE Conference on Computer Communications (INFOCOM), pp. 1346–1354. IEEE (2015)

    Google Scholar 

  7. Dinur, I., Safra, S.: On the hardness of approximating minimum vertex cover. Ann. Math. 162, 439–485 (2005)

    Article  MathSciNet  Google Scholar 

  8. Dinur, I., Steurer, D.: Analytical approach to parallel repetition. In: Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 624–633. ACM, New York (2014). https://doi.org/10.1145/2591796.2591884. http://doi.acm.org/10.1145/2591796.2591884

  9. Even, G., Medina, M., Patt-Shamir, B.: Competitive path computation and function placement in SDNs. arXiv preprint arXiv:1602.06169 (2016)

  10. Even, G., Rost, M., Schmid, S.: An approximation algorithm for path computation and function placement in SDNs. In: Suomela, J. (ed.) SIROCCO 2016. LNCS, vol. 9988, pp. 374–390. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-48314-6_24

    Chapter  MATH  Google Scholar 

  11. Fayazbakhsh, S.K., Chiang, L., Sekar, V., Yu, M., Mogul, J.C.: Enforcing network-wide policies in the presence of dynamic middlebox actions using flowtags. In: 11th USENIX Symposium on Networked Systems Design and Implementation (NSDI 2014), pp. 543–546. USENIX Association, Seattle, April 2014. https://www.usenix.org/conference/nsdi14/technical-sessions/presentation/fayazbakhsh

  12. Feige, U.: A threshold of ln n for approximating set cover. J. ACM (JACM) 45(4), 634–652 (1998)

    Article  Google Scholar 

  13. Forrest, J.: Clp: Coin-or linear program solver. In: DIMACS Workshop on COIN-OR, pp. 17–20, July 2006

    Google Scholar 

  14. Gember-Jacobson, A., et al.: OpenNF: enabling innovation in network function control. In: Proceedings of the ACM Conference on SIGCOMM, pp. 163–174. ACM (2014). https://doi.org/10.1145/2619239.2626313. http://doi.acm.org/10.1145/2619239.2626313

  15. Heorhiadi, V., Reiter, M.K., Sekar, V.: Accelerating the development of software-defined network optimization applications using SOL. arXiv preprint arXiv:1504.07704 (2015)

  16. Heorhiadi, V., Reiter, M.K., Sekar, V.: Simplifying software-defined network optimization using sol. In: 13th USENIX Symposium on Networked Systems Design and Implementation (NSDI 2016), pp. 223–237. USENIX Association, Santa Clara, March 2016. https://www.usenix.org/conference/nsdi16/technical-sessions/presentation/heorhiadi

  17. Jin, Y., Wen, Y., Westphal, C.: Towards joint resource allocation and routing to optimize video distribution over future internet. In: IFIP Networking Conference (IFIP Networking) 2015, 1–9 May 2015. https://doi.org/10.1109/IFIPNetworking.2015.7145311

  18. Khot, S., Regev, O.: Vertex cover might be hard to approximate to within 2-\(\varepsilon \). J. Comput. Syst. Sci. 74(3), 335–349 (2008)

    Google Scholar 

  19. Li, X., Qian, C.: A survey of network function placement. In: 13th IEEE Annual Consumer Communications Networking Conference (CCNC), pp. 948–953, January 2016. https://doi.org/10.1109/CCNC.2016.7444915

  20. Lukovszki, T., Rost, M., Schmid, S.: Approximate and incremental network function placement. J. Parallel Distrib. Comput. 120, 159–169 (2018)

    Article  Google Scholar 

  21. Martins, J., et al.: Clickos and the art of network function virtualization. In: 11th USENIX Symposium on Networked Systems Design and Implementation (NSDI 2014), pp. 459–473. USENIX Association, April 2014. https://www.usenix.org/conference/nsdi14/technical-sessions/presentation/martins

  22. OPNFV: OPNFV: an open platform to accelerate NFV, Linux Foundation. https://www.opnfv.org/

  23. Orlowski, S., Wessäly, R., Pióro, M., Tomaszewski, A.: Sndlib 1.0—survivable network design library. Networks 55(3), 276–286 (2010)

    Google Scholar 

  24. Qazi, Z.A., Tu, C.C., Chiang, L., Miao, R., Sekar, V., Yu, M.: SIMPLE-fying middlebox policy enforcement using SDN. In: Proceedings of ACM SIGCOMM, pp. 27–38. ACM (2013). https://doi.org/10.1145/2486001.2486022. http://doi.acm.org/10.1145/2486001.2486022

  25. Rajagopalan, S., Williams, D., Jamjoom, H., Warfield, A.: Split/merge: system support for elastic execution in virtual middleboxes. In: Presented as Part of the 10th USENIX Symposium on Networked Systems Design and Implementation (NSDI 2013), pp. 227–240. USENIX, Lombard (2013). https://www.usenix.org/conference/nsdi13/technical-sessions/presentation/rajagopalan

  26. Rost, M., Schmid, S.: Charting the complexity landscape of virtual network embeddings. In: IFIP Networking, May 2018. http://eprints.cs.univie.ac.at/5580/

  27. Rost, M., Schmid, S.: Virtual network embedding approximations: leveraging randomized rounding. In: IFIP Networking, May 2018. http://eprints.cs.univie.ac.at/5579/

  28. Sekar, V., Egi, N., Ratnasamy, S., Reiter, M.K., Shi, G.: Design and implementation of a consolidated middlebox architecture. In: Proceedings of the 9th USENIX Conference on Networked Systems Design and Implementation, NSDI 2012, p. 24. USENIX Association (2012). http://dl.acm.org/citation.cfm?id=2228298.2228331

  29. Sherry, J., Hasan, S., Scott, C., Krishnamurthy, A., Ratnasamy, S., Sekar, V.: Making middleboxes someone else’s problem: network processing as a cloud service. In: Proceedings of the ACM SIGCOMM 2012 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, SIGCOMM 2012, pp. 13–24. ACM (2012). https://doi.org/10.1145/2342356.2342359. http://doi.acm.org/10.1145/2342356.2342359

  30. Sviridenko, M.: A note on maximizing a submodular set function subject to a knapsack constraint. Oper. Res. Lett. 32(1), 41–43 (2004)

    Article  MathSciNet  Google Scholar 

  31. Uhlig, S., Quoitin, B., Lepropre, J., Balon, S.: Providing public intradomain traffic matrices to the research community. ACM SIGCOMM Comput. Commun. Rev. 36(1), 83–86 (2006)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Stanford University, Stanford, CA, USA

    Moses Charikar

  2. Amazon.com, East Palo Alto, CA, USA

    Yonatan Naamad

  3. Princeton University, Princeton, NJ, USA

    Jenifer Rexford

  4. ByteDance, Seattle, WA, USA

    X. Kelvin Zou

Authors
  1. Moses Charikar
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  2. Yonatan Naamad
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  3. Jenifer Rexford
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  4. X. Kelvin Zou
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Corresponding author

Correspondence to Yonatan Naamad .

Editor information

Editors and Affiliations

  1. Technical University of Darmstadt, Darmstadt, Germany

    Yann Disser

  2. Hellenic Open University, Patras, Greece

    Vassilios S. Verykios

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Charikar, M., Naamad, Y., Rexford, J., Zou, X.K. (2019). Multi-commodity Flow with In-Network Processing. In: Disser, Y., Verykios, V. (eds) Algorithmic Aspects of Cloud Computing. ALGOCLOUD 2018. Lecture Notes in Computer Science(), vol 11409. Springer, Cham. https://doi.org/10.1007/978-3-030-19759-9_6

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  • DOI: https://doi.org/10.1007/978-3-030-19759-9_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-19758-2

  • Online ISBN: 978-3-030-19759-9

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