Reconfigurable networks are a novel communication paradigm in which the pattern of connectivity between hosts varies rapidly over time. Prior theoretical work explored the inherent tradeoffs between throughput (or, hop-count) and latency, and showed the existence of infinitely many Pareto-optimal designs as the network size tends to infinity. Existing Pareto-optimal designs use a connection schedule which is fine-tuned to the desired hop-count \(h\), permitting lower latency as \(h\) increases. However, in reality datacenter workloads contain a mix of low-latency and high-latency requests. Using a connection schedule fine-tuned for one request type leads to inefficiencies when serving other types.

Reconfigurable datacenter networks use fast optical circuit switches to provide high bandwidths at low cost, therefore emerging as a compelling alternative to packet switching. These switches offer micro- and nano-second reconfiguration, and reacting to demand at this time scale is infeasible. Proposed designs have therefore largely been oblivious, supporting arbitrary traffic patterns. However, this imposes a fundamental latency-throughput tradeoff that significantly limits the benefits of these switches.

Circuit-switched technologies have long been proposed for handling high-throughput traffic in datacenter networks, but recent developments in nanosecond-scale reconfiguration have created the enticing possibility of handling low-latency traffic as well. The novel Oblivious Reconfigurable Network (ORN) design paradigm promises to deliver on this possibility. Prior work in ORN designs achieved latencies that scale linearly with system size, making them unsuitable for large-scale deployments. Recent theoretical work showed that ORNs can achieve far better latency scaling, proposing theoretical ORN designs that are Pareto optimal in latency and throughput.

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.

Traditional datacenter networks have been designed primarily using packet switches. However, due to the end of Moore's Law and Denard Scaling, packet switches face increasing difficulty in scaling to meet network demands without consuming unnecessarily large amounts of power, both within high-density racks[14] and throughout the datacenter[1]. As a result, many emerging network designs have intentionally avoided using packet switches [5, 7, 9, 10, 12, 15, 16]. Circuit switches present an exciting alternative to packet switches due to their reduced power consumption[1, 14], and potential to scale to arbitrary bandwidth (in the case of optical switches). While slow reconfiguration times have historically made circuit switches unable to support low-latency traffic, recent circuit switch design have emerged that are capable of nanosecond-scale reconfiguration times, including both electrical [11] and optical [3, 4, 6] switches. Unfortunately, conventional, dynamically-reconfiguring circuit-switched network designs have inherent latencies both for computing which circuits to deploy and for coordinating switches and nodes, limiting the benefits of this new capability.

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.