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1. Multi-Path Routing in the Jellyfish Network

   Alzaid, Zaid; Bhowmik, Saptarshi; Yuan, Xin (January 2021, IPDPS workshop on Scalable Networks for Advanced Computer Systems)

   null (Ed.)

   The Jellyfish network has recently been proposed as an alternative to the fat-tree network for data centers and high-performance computing clusters. Jellyfish uses a random regular graph as its switch-level topology and has shown to be more cost-effective than fat-trees. Effective routing on Jellyfish is challenging. It is known that shortest path routing and equal cost multi-path routing (ECMP) do not work well on Jellyfish. Existing schemes use variations of k-shortest path routing (KSP). In this work, we study two routing components for Jellyfish: path selection that decides the paths to route traffic, and routing mechanisms that decide which path to be used for each packet. We show that the performance of the existing KSP can be significantly improved by incorporating two heuristics, randomization and edge-disjointness. We evaluate a range of routing mechanisms, including traffic oblivious and traffic adaptive schemes, and identify an adaptive routing scheme with noticeably higher performance than others. 

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2. Optimal oblivious reconfigurable networks

   https://doi.org/10.1145/3519935.3520020  

   Amir, Daniel; Wilson, Tegan; Shrivastav, Vishal; Weatherspoon, Hakim; Kleinberg, Robert; Agarwal, Rachit (June 2022, ACM SIGACT Symposium on Theory of Computing)

   Oblivious routing has a long history in both the theory and practice of networking. In this work we initiate the formal study of oblivious routing in the context of reconfigurable networks, a new architecture that has recently come to the fore in datacenter networking. These networks allow a rapidly changing bounded-degree pattern of interconnections between nodes, but the network topology and the selection of routing paths must both be oblivious to the traffic demand matrix. Our focus is on the trade-off between maximizing throughput and minimizing latency in these networks. For every constant throughput rate, we characterize (up to a constant factor) the minimum latency achievable by an oblivious reconfigurable network design that satisfies the given throughput guarantee. The trade-off between these two objectives turns out to be surprisingly subtle: the curve depicting it has an unexpected scalloped shape reflecting the fact that load-balancing becomes more difficult when the average length of routing paths is not an integer because equalizing all the path lengths is not possible. The proof of our lower bound uses LP duality to verify that Valiant load balancing is the most efficient oblivious routing scheme when used in combination with an optimally-designed reconfigurable network topology. The proof of our upper bound uses an algebraic construction in which the network nodes are identified with vectors over a finite field, the network topology is described by either the elementary basis or a sequence of Vandermonde matrices, and routing paths are constructed by selecting columns of these matrices to yield the appropriate mixture of path lengths within the shortest possible time interval. 

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3. Breaking the VLB Barrier for Oblivious Reconfigurable Networks

   https://doi.org/10.1145/3618260.3649608  

   Wilson, Tegan; Amir, Daniel; Saran, Nitika; Kleinberg, Robert; Shrivastav, Vishal; Weatherspoon, Hakim (June 2024, Conference proceedings of the annual ACM Symposium on Theory of Computing)

   In a landmark 1981 paper, Valiant and Brebner gave birth to the study of oblivious routing and, simultaneously, introduced its most powerful and ubiquitous method: Valiant load balancing (VLB). By routing messages through a randomly sampled intermediate node, VLB lengthens routing paths by a factor of two but gains the crucial property of obliviousness: it balances load in a completely decentralized manner, with no global knowledge of the communication pattern. Forty years later, with datacenters handling workloads whose communication pattern varies too rapidly to allow centralized coordination, oblivious routing is as relevant as ever, and VLB continues to take center stage as a widely used — and in some settings, provably optimal — way to balance load in the network obliviously to the traffic demands. However, the ability of the network to rapidly reconfigure its interconnection topology gives rise to new possibilities. In this work we revisit the question of whether VLB remains optimal in the novel setting of reconfigurable networks. Prior work showed that VLB achieves the optimal tradeoff between latency and guaranteed throughput. In this work we show that a strictly superior latency-throughput tradeoff is achievable when the throughput bound is relaxed to hold with high probability. The same improved tradeoff is also achievable with guaranteed throughput under time-stationary demands, provided the latency bound is relaxed to hold with high probability and that the network is allowed to be semi-oblivious, using an oblivious (randomized) connection schedule but demand-aware routing. We prove that the latter result is not achievable by any fully-oblivious reconfigurable network design, marking a rare case in which semi-oblivious routing has a provable asymptotic advantage over oblivious routing. Our results are enabled by a novel oblivious routing scheme that improves VLB by stretching routing paths the minimum possible amount — an additive stretch of 1 rather than a multiplicative stretch of 2 — yet still manages to balance load with high probability when either the traffic demand matrix or the network’s interconnection schedule are shuffled by a uniformly random permutation. To analyze our routing scheme we prove an exponential tail bound which may be of independent interest, concerning the distribution of values of a bilinear form on an orbit of a permutation group action. 

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4. A Constrained Shortest Path Scheme for Virtual Network Service Management

   https://doi.org/10.1109/TNSM.2018.2865204  

   Chemodanov, Dmitrii; Esposito, Flavio; Calyam, Prasad; Sukhov, Andrei (August 2018, IEEE Transactions on Network and Service Management)

   Virtual network services that span multiple data centers are important to support emerging data-intensive applications in fields such as bioinformatics and retail analytics. Successful virtual network service composition and maintenance requires flexible and scalable ‘constrained shortest path management’ both in the management plane for virtual network embedding (VNE) or network function virtualization service chaining (NFV-SC), as well as in the data plane for traffic engineering (TE). In this paper, we show analytically and empirically that leveraging constrained shortest paths within recent VNE, NFV-SC and TE algorithms can lead to network utilization gains (of up to 50%) and higher energy efficiency. The management of complex VNE, NFV-SC and TE algorithms can be, however, intractable for large scale substrate networks due to the NP-hardness of the constrained shortest path problem. To address such scalability challenges, we propose a novel, exact constrained shortest path algorithm viz.‘, Neighborhoods Method’ (NM). Our NM uses novel search space reduction techniques and has a theoretical quadratic speed-up making it practically faster (by an order of magnitude) than recent branch-and-bound exhaustive search solutions. Finally, we detail our NM-based SDN controller implementation in a real-world testbed to further validate practical NM benefits for virtual network services. 

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5. Improving Valiant Routing for Slim Fly Networks

   https://doi.org/10.1109/ICPPW.2017.33  

   Han, Deyu; Wang, Zhaofeng; Bunde, David P. (August 2017, 2017 46th International Conference on Parallel Processing Workshops (ICPPW))

   Valiant routing, the use of a random intermediate node to distribute network traffic, has been proposed for a number of recent HPC network topologies. It is also commonly used as a bulding block for adaptive routing algorithms, which use shortest path routes when possible, but revert to Valiant routing when necessary to avoid hot spots. We show that the version of Valiant routing proposed for the Slim fly topology can cause messages to follow loops, using an edge in both directions before returning to edges of the original shortest path. Removing these loops in the UGAL-L adaptive routing algorithm is shown to provide slight improvements in average latency and also allow the network to carry up to 12% more traffic before saturation. 

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