arXiv subjects

Tegan Wilson

Publications and source records attributed to Tegan Wilson.

5 recordsLinked to original sources

arXiv2026

On Topology's Role in ML Training Performance

Modern machine learning training workloads run on large-scale networks of compute accelerators. The networks commonly deployed in these systems are typically variations of two basic topologies: the fat-tree Clos and the torus. In this paper, we derive analytical results the elucidate how the choice of topology shapes achievable performance for the small set of collective communication operations that underlies modern machine learning workloads. We also consider how these results change when we include additional factors such as network failures and job placement strategies. Overall, we find that one topology does not dominate in all cases, but that the Clos achieves better collective completion time in most cases and provides benefits in resilience and flexibility.

cs.NI↗

arXiv2025

Indirect Coflow Scheduling

We consider routing in reconfigurable networks, which is also known as coflow scheduling in the literature. The algorithmic literature generally (perhaps implicitly) assumes that the amount of data to be transferred is large. Thus the standard way to model a collection of requested data transfers is by an integer demand matrix $D$, where the entry in row $i$ and column $j$ of $D$ is an integer representing the amount of information that the application wants to send from machine/node $i$ to machine/node $j$. A feasible coflow schedule is then a sequence of matchings, which represent the sequence of data transfers that covers $D$. In this work, we investigate coflow scheduling when the size of some of the requested data transfers may be small relative to the amount of data that can be transferred in one round. fractional matchings and/or that employ indirect routing, and compare the relative utility of these options. We design algorithms that perform much better for small demands than the algorithms in the literature that were designed for large data transfers.

cs.DS↗

arXiv2025

Universal Connection Schedules for Reconfigurable Networking

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. A more flexible and efficient alternative is a {\em universal schedule}, a single connection schedule capable of attaining many Pareto-optimal tradeoff points simultaneously, merely by varying the choice of routing paths. In this work we present the first universal schedules for oblivious routing. Our constructions yield universal schedules which are near-optimal for all possible hop-counts $h$. The key technical idea is to specialize to a type of connection schedule based on cyclic permutations and to develop a novel Fourier-analytic method for analyzing randomized routing on these connection schedules. We first show that a uniformly random connection schedule suffices with multiplicative error in throughput, and latency optimal up to a $\log N$ factor. We then show that a more carefully designed random connection schedule suffices with additive error in throughput, but improved latency optimal up to only constant factors. Finally, we show that our first randomized construction can be made deterministic using a derandomized version of the Lovett-Meka discrepancy minimization algorithm to obtain the same result.

cs.DS↗

arXiv2023

Breaking the VLB Barrier for Oblivious Reconfigurable Networks

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. Forty years later, with datacenters handling workloads whose communication pattern varies too rapidly to allow centralized coordination, VLB continues to take center stage as a widely used - and in some cases 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. 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.

cs.DS↗

arXiv2021

Optimal Oblivious Reconfigurable Networks

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.

cs.DS↗