Optimal Oblivious Routing for Structured Networks
Authors: 
Sucha Supittayapornpong, Pooria Namyar, Mingyang Zhang, Minlan Yu, 
Ramesh GovindanAuthors Info & Claims
Sucha Supittayapornpong, Pooria Namyar, Mingyang Zhang, Minlan Yu, Ramesh GovindanAuthors Info & ClaimsPages 1988 - 1997
Abstract
Oblivious routing distributes traffic from sources to destinations following predefined routes with rules independent of traffic demands. While finding optimal oblivious routing is intractable for general topologies, we show that it is tractable for structured topologies often used in datacenter networks. To achieve this, we apply graph automorphism and prove the existence of the optimal automorphism-invariant solution. This result reduces the search space to targeting the optimal automorphism-invariant solution. We design an iterative algorithm to obtain such a solution by alternating between two linear programs. The first program finds an automorphism-invariant solution based on representative variables and constraints, making the problem tractable. The second program generates adversarial demands to ensure the final result satisfies all possible demands. Since, the construction of the representative variables and constraints are combinatorial problems, we design polynomial-time algorithms for the construction. We evaluate proposed iterative algorithm in terms of throughput performance, scalability, and generality over three potential applications. The algorithm i) improves the throughput up to 87.5% over a heuristic algorithm for partially deployed FatTree, ii) scales for FatClique with a thousand switches, iii) is applicable to a general structured topology with non-uniform link capacity and server distribution.
References
[1]
M. Al-Fares, A. Loukissas, and A. Vahdat, “A scalable, commodity data center network architecture,” SIGCOMM Comput. Commun. Rev., vol. 38, no. 4, pp. 63–74, Aug. 2008. [Online]. Available: https://doi.org/10.1145/1402946.1402967
[2]
A. Greenberg, J. R. Hamilton, N. Jain, S. Kandula, C. Kim, P. Lahiri, D. A. Maltz, P. Patel, and S. Sengupta, “Vl2: A scalable and flexible data center network,” SIGCOMM Comput. Commun. Rev., vol. 39, no. 4, pp. 51–62, Aug. 2009. [Online]. Available: https://doi.org/10.1145/1594977.1592576
[3]
A. Singh, J. Ong, A. Agarwal, G. Anderson, A. Armistead, R. Bannon, S. Boving, G. Desai, B. Felderman, P. Germano, A. Kanagala, J. Provost, J. Simmons, E. Tanda, J. Wanderer, U. Hölzle, S. Stuart, and A. Vahdat, “Jupiter rising: A decade of clos topologies and centralized control in google’s datacenter network,” SIGCOMM Comput. Commun. Rev., vol. 45, no. 4, pp. 183–197, Aug. 2015. [Online]. Available: https://doi.org/10.1145/2829988.2787508
[4]
A. Andreyev. Introducing data center fabric, the next-generation facebook data center network. [Online]. Available: https://engineering.fb.com/2014/11/14/production-engineering/introducing-data-center-fabric-the-next-generation-facebook-data-center-network/
[5]
J. H. Ahn, N. Binkert, A. Davis, M. McLaren, and R. S. Schreiber, “Hyperx: Topology, routing, and packaging of efficient large-scale networks,” in Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis, ser. SC ’09. New York, NY, USA: Association for Computing Machinery, 2009. [Online]. Available: https://doi.org/10.1145/1654059.1654101
[6]
J. Kim, W. J. Dally, S. Scott, and D. Abts, “Technology-driven, highly-scalable dragonfly topology,” in 2008 International Symposium on Computer Architecture, 2008, pp. 77–88.
[7]
M. Besta and T. Hoefler, “Slim fly: A cost effective low-diameter network topology,” in SC ’14: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, 2014, pp. 348–359.
[8]
A. Singla, C.-Y. Hong, L. Popa, and P. B. Godfrey, “Jellyfish: Networking data centers randomly,” in 9th USENIX Symposium on Networked Systems Design and Implementation (NSDI 12). San Jose, CA: USENIX Association, Apr. 2012, pp. 225–238. [On-line]. Available: https://www.usenix.org/conference/nsdi12/technical-sessions/presentation/singla
[9]
A. Valadarsky, G. Shahaf, M. Dinitz, and M. Schapira, “Xpander: Towards optimal-performance datacenters,” in Proceedings of the 12th International on Conference on Emerging Networking EXperiments and Technologies, ser. CoNEXT ’16. New York, NY, USA: Association for Computing Machinery, 2016, pp. 205–219. [Online]. Available: https://doi.org/10.1145/2999572.2999580
[10]
A. Singla, P. B. Godfrey, and A. Kolla, “High throughput data center topology design,” in 11th USENIX Symposium on Networked Systems Design and Implementation (NSDI 14). Seattle, WA: USENIX Association, Arp. 2014, pp. 29–41. [On-line]. Available: https://www.usenix.org/conference/nsdi14/technical-sessions/presentation/singla
[11]
M. Zhang, R. N. Mysore, S. Supittayapornpong, and R. Govindan, “Understanding lifecycle management complexity of datacenter topologies,” in 16th USENIX Symposium on Networked Systems Design and Implementation (NSDI 19). Boston, MA: USENIX Association, Feb. 2019, pp. 235–254. [Online]. Available: https://www.usenix.org/conference/nsdi19/presentation/zhang
[12]
V. Harsh, S. A. Jyothi, and P. B. Godfrey, “Spineless data centers,” in Proceedings of the 19th ACM Workshop on Hot Topics in Networks, ser. HotNets ’20. New York, NY, USA: Association for Computing Machinery, 2020, pp. 67–73. [Online]. Available: https://doi.org/10.1145/3422604.3425945
[13]
D. Thaler and C. Hopps. Rfc2991: Multipath issues in unicast and multicast next-hop selection. [Online]. Available: https://datatracker.ietf.org/doc/html/rfc2991
[14]
R. Zhang-Shen and N. McKeown, “Guaranteeing quality of service to peering traffic,” in IEEE INFOCOM 2008 - The 27th Conference on Computer Communications, 2008, pp. 1472–1480.
[15]
M. Kodialam, T. V. Lakshman, J. B. Orlin, and S. Sengupta, “Preconfiguring ip-over-optical networks to handle router failures and unpredictable traffic,” IEEE Journal on Selected Areas in Communications, vol. 25, no. 5, pp. 934–948, 2007.
[16]
M. Al-Fares, S. Radhakrishnan, B. Raghavan, N. Huang, and A. Vahdat, “Hedera: Dynamic flow scheduling for data center networks,” in Proceedings of the 7th USENIX Conference on Networked Systems Design and Implementation, ser. NSDI’10. USA: USENIX Association, 2010, p. 19.
[17]
A. Roy, H. Zeng, J. Bagga, G. Porter, and A. C. Snoeren, “Inside the social network’s (datacenter) network,” SIGCOMM Comput. Commun. Rev., vol. 45, no. 4, pp. 123–137, Aug. 2015. [Online]. Available: https://doi.org/10.1145/2829988.2787472
[18]
C. Guo, H. Wu, K. Tan, L. Shi, Y. Zhang, and S. Lu, “Dcell: A scalable and fault-tolerant network structure for data centers,” in SIGCOMM08. Association for Computing Machinery, Inc., August 2008. [Online]. Available: https://www.microsoft.com/en-us/research/publication/dcell-a-scalable-and-fault-tolerant-network-structure-for-data-centers/
[19]
C. Guo, G. Lu, D. Li, H. Wu, X. Zhang, Y. Shi, C. Tian, Y. Zhang, S. Lu, and G. Lv, “Bcube: A high performance, server-centric network architecture for modular data centers,” in ACM SIGCOMM. Association for Computing Machinery, Inc., August 2009. [Online]. Available: https://www.microsoft.com/en-us/research/publication/bcube-a-high-performance-server-centric-network-architecture-for-modular-data-centers/
[20]
Broadcom. Tomahawk4 / bcm56990 series. [On-line]. Available: https://www.broadcom.com/products/ethernet-connectivity/switching/strataxgs/bcm56990-series
[21]
P. Namyar, S. Supittayapornpong, M. Zhang, M. Yu, and R. Govindan, “A throughput-centric view of the performance of datacenter topologies,” in Proceedings of the 2021 ACM SIGCOMM 2021 Conference, ser. SIGCOMM ’21. New York, NY, USA: Association for Computing Machinery, 2021, p. 349–369. [Online]. Available: https://doi.org/10.1145/3452296.3472913
[22]
S. Supittayapornpong, B. Raghavan, and R. Govindan, “Towards highly available clos-based wan routers,” in Proceedings of the ACM Special Interest Group on Data Communication, ser. SIGCOMM ’19. New York, NY, USA: Association for Computing Machinery, 2019, p. 424–440. [Online]. Available: https://doi.org/10.1145/3341302.3342086
[23]
D. Applegate and E. Cohen, “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, ser. SIGCOMM ’03. New York, NY, USA: Association for Computing Machinery, 2003, p. 313–324. [Online]. Available: https://doi.org/10.1145/863955.863991
[24]
B. Towles and W. Dally, “Worst-case traffic for oblivious routing functions,” IEEE Computer Architecture Letters, vol. 1, no. 1, pp. 4–4 2002.
[25]
S. A. Jyothi, A. Singla, P. B. Godfrey, and A. Kolla, “Measuring and understanding throughput of network topologies,” in SC ’16: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, 2016, pp. 761–772.
[26]
B. D. McKay and A. Piperno, “Practical graph isomorphism, ii,” Journal of Symbolic Computation, vol. 60, pp. 94–112, 2014. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0747717113001193
[27]
Gurobi Optimization, LLC, “Gurobi Optimizer Reference Manual,” 2021. [Online]. Available: https://www.gurobi.com
[28]
J. Zhou, M. Tewari, M. Zhu, A. Kabbani, L. Poutievski, A. Singh, and A. Vahdat, “Wcmp: Weighted cost multipathing for improved fairness in data centers,” in Proceedings of the Ninth European Conference on Computer Systems, ser. EuroSys ’14. New York, NY, USA: Association for Computing Machinery, 2014. [Online]. Available: https://doi.org/10.1145/2592798.2592803
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