VirtuCast: Multicast and Aggregation with In-Network Processing

An Exact Single-Commodity Algorithm
  • Matthias Rost
  • Stefan Schmid
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8304)

Abstract

As the Internet becomes more virtualized and software-defined, new functionality is introduced in the network core: the distributed resources available in ISP central offices, universal nodes, or datacenter middleboxes can be used to process (e.g., filter, aggregate or duplicate) data. Based on this new networking paradigm, we formulate the Constrained Virtual Steiner Arborescence Problem (CVSAP) which asks for optimal locations to perform in-network processing, in order to jointly minimize processing costs and network traffic while respecting link and node capacities.

We prove that CVSAP cannot be approximated (unless NP ⊆ P), and accordingly, develop the exact algorithm VirtuCast to compute optimal solutions to CVSAP. VirtuCast consists of: (1) a compact single-commodity flow Integer Programming (IP) formulation; (2) a flow decomposition algorithm to reconstruct individual routes from the IP solution. The compactness of the IP formulation allows for computing lower bounds even on large instances quickly, speeding up the algorithm significantly. We rigorously prove VirtuCast’s correctness and show its applicability to solve realistically sized instances close to optimality.

Keywords

Network Virtualization Network Functions Virtualization Multicast In-Network Aggregation Data-Center Middleboxes ISP Integer Programming 

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References

  1. 1.
    Achterberg, T.: SCIP: Solving Constraint Integer Programs. Mathematical Programming Computation 1(1), 1–41 (2009)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms and Applications. Prentice Hall (1993)Google Scholar
  3. 3.
    Banchs, A., Effelsberg, W., Tschudin, C., Turau, V.: Multicasting Multimedia Streams with Active Networks. In: Proc. Local Computer Network Conference (LCN). IEEE (1998)Google Scholar
  4. 4.
    Cai, Z., Lin, G., Xue, G.: Improved Approximation Algorithms for the Capacitated Multicast Routing Problem. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 136–145. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Costa, P., Donnelly, A., Rowstron, A., Shea, G.O.: Camdoop: Exploiting In-network Aggregation for Big Data Applications. In: Proc. USENIX Symposium on Networked Systems Design and Implementation (NSDI) (2012)Google Scholar
  6. 6.
    Costa, P., Migliavacca, M., Pietzuch, P., Wolf, A.L.: NaaS: Network-as-a-Service in the Cloud. In: Proc. USENIX Hot-ICE Workshop (2012)Google Scholar
  7. 7.
    Cranor, C., Johnson, T., Spataschek, O., Shkapenyuk, V.: Gigascope: A Stream Database for Network Applications. In: Proc. ACM SIGMOD International Conference on Management of Data, pp. 647–651 (2003)Google Scholar
  8. 8.
    Demaine, E.D., Hajiaghayi, M., Klein, P.N.: Node-weighted steiner tree and group steiner tree in planar graphs. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part I. LNCS, vol. 5555, pp. 328–340. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    European Telecommunications Standards Institute. Network Functions Virtualisation - Introductory White Paper. SDN and OpenFlow World Congress, Darmstadt-Germany (2012)Google Scholar
  10. 10.
    Eyal, I., Keidar, I., Patterson, S., Rom, R.: In-Network Analytics for Ubiquitous Sensing. In: Afek, Y. (ed.) DISC 2013. LNCS, vol. 8205, pp. 507–521. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  11. 11.
    Fasolo, E., Rossi, M., Widmer, J., Zorzi, M.: In-Network Aggregation Techniques for Wireless Sensor Networks: A Survey. IEEE Wireless Communications 14, 70–87 (2007)CrossRefGoogle Scholar
  12. 12.
    Goemans, M.X., Myung, Y.-S.: A catalog of Steiner tree formulations. Networks 23(1), 19–28 (1993)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Gollowitzer, S., Ljubić, I.: MIP models for Connected Facility Location: A theoretical and computational study. Computers & Operations Research 38(2), 435–449 (2011)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Hermsmeyer, C., Hernandez-Valencia, E., Stoll, D., Tamm, O.: Ethernet aggregation and core network models for effcient and reliable IPTV services. Bell Labs Technical Journal 12(1), 57–76 (2007)CrossRefGoogle Scholar
  15. 15.
    Johnson, D.S., Minkoff, M., Phillips, S.: The prize collecting Steiner tree problem: theory and practice. In: Proc. 11th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 760–769. Society for Industrial and Applied Mathematics (2000)Google Scholar
  16. 16.
    Koch, T., Martin, A.: Solving Steiner tree problems in graphs to optimality. Networks 32(3), 207–232 (1998)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Lee, Y., Lu, L., Qiu, Y., Glover, F.: Strong formulations and cutting planes for designing digital data service networks. Telecommunication Systems 2(1), 261–274 (1993)CrossRefGoogle Scholar
  18. 18.
    Lucena, A., Resende, M.G.: Strong lower bounds for the prize collecting Steiner problem in graphs. Discrete Applied Mathematics 141(1), 277–294 (2004)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Molnár, M.: Hierarchies to Solve Constrained Connected Spanning Problems. Technical Report lrimm-00619806, University Montpellier 2, LIRMM (2011)Google Scholar
  20. 20.
    Narayana, S., Jiang, W., Rexford, J., Chiang, M.: Joint Server Selection and Routing for Geo-Replicated Services. In: Proc. Workshop on Distributed Cloud Computing (DCC) (2013)Google Scholar
  21. 21.
    Oliveira, C., Pardalos, P.: Streaming Cache Placement. In: Mathematical Aspects of Network Routing Optimization. Springer Optimization and Its Applications, pp. 117–133. Springer, New York (2011)CrossRefGoogle Scholar
  22. 22.
    Park, J.-W., Lim, H., Kim, J.: Virtual-node-based multicast routing and wavelength assignment in sparse-splitting optical networks. Photonic Network Communications 19(2), 182–191 (2010)CrossRefGoogle Scholar
  23. 23.
    Qazi, Z., Tu, C.-C., Chiang, L., Miao, R., Sekar, V., Yu, M.: SIMPLE-fying Middlebox Policy Enforcement Using SDN. In: Proc. ACM SIGCOMM (2013)Google Scholar
  24. 24.
    Quoitin, B., Van den Schrieck, V., Franois, P., Bonaventure, O.: IGen: Generation of router-level Internet topologies through network design heuristics. In: Proc. 21st International Teletraffic Congress (ITC), pp. 1–8 (2009)Google Scholar
  25. 25.
    Rost, M., Schmid, S.: CVSAP-Project Website (2013), http://www.net.t-labs.tu-berlin.de/~stefan/cvsap.html
  26. 26.
    Rost, M., Schmid, S.: The Constrained Virtual Steiner Arborescence Problem: Formal Definition, Single-Commodity Integer Programming Formulation and Computational Evaluation. Technical report, arXiv: 1310.0346 (2013)Google Scholar
  27. 27.
    Shi, S.: A Proposal for A Scalable Internet Multicast Architecture. Technical Report WUCS-01-03, Washington University (2001)Google Scholar
  28. 28.
    Voß, S.: Steiner Tree Problems in Telecommunications. In: Handbook of optimization in telecommunications, ch. 18. Spinger Science + Business Media, New York (2006)Google Scholar
  29. 29.
    Zhang, Z., Zhang, M., Greenberg, A., Hu, Y.C., Mahajan, R., Christian, B.: Optimizing cost and performance in online service provider networks. In: Proc. 7th USENIX Conference on Networked Systems Design and Implementation (NSDI) (2010)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Matthias Rost
    • 1
  • Stefan Schmid
    • 1
  1. 1.Telekom Innovation Laboratories (T-Labs)TU BerlinGermany

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