Randomization and augmentation improve machine scheduling accuracy
Gaps and Augmentations in Bayesian Scheduling
Computer Science and Game Theory
Summary
Scheduling jobs fairly and efficiently across different machines is a tricky problem that gets harder when machines act selfishly. The authors study how adding prior knowledge, allowing machines to randomize decisions, and letting machines use extra resources can help improve scheduling. They show that random choices can strictly improve fairness and efficiency in some cases, and that giving machines more options or copies leads to near-perfect scheduling. Their work builds on foundational results and shows new ways to overcome known limits in scheduling algorithms.
What this means in practice
- •For cloud platform engineers: Use randomized Bayesian mechanisms to improve fair job distribution across unrelated computing nodes.
- •For data center operators: Leverage machine-side replicas or augmented resources to achieve near-optimal scheduling fairness and efficiency.
A theory result. No direct application yet.
Authors
Ahuva Mu'alem
Abstract
The recent resolution of the Nisan--Ronen conjecture~\cite{NR,CKK} establishes that the optimal worst-case approximation ratio of deterministic truthful mechanisms for makespan on m unrelated machines is exactly m. We ask how prior information, Bayesian incentive compatibility (BIC), randomization, and machine-side resource augmentation change this barrier. We obtain three main results. First, we prove an asymptotic 4/3 lower bound for randomized BIC mechanisms with two machines, strengthening the previous 1.2 deterministic-BIC lower bound~\cite{MS}. Second, in the prior-free setting for two machines, randomization improves the known truthful ratio from 2 to 7/4~\cite{NR}. We show that randomized BIC scheduling mechanisms are likewise strictly more powerful than their deterministic counterparts, exhibiting an asymptotic BIC-integrality gap of 8/7. Thus, optimality in prior-dependent BIC scheduling can strictly require randomization. This parallels the role of lotteries in multidimensional revenue maximization, where randomization can strictly improve revenue~\cite{MV,BCKW}. Third, we show that when job assignments are sufficiently well spread across machines (more formally, when the pairwise collision parameter $Δ_r$ is bounded by a constant independent of both the number of machines m and the number of sampled layers r), then $O(m/\varepsilon)$ sampled layers suffice for the standard truthful MinWork mechanism to achieve a $1+\varepsilon$-approximation to the original first-best benchmark. Equivalently, $O(m/\varepsilon)$ sampled replicas per machine suffice. This resource-augmentation result parallels the Bulow--Klemperer perspective~\cite{BK,EFFTW}. As a by-product, in the standard unaugmented model, MinWork achieves a $(1+\frac{Δ_1(m-1)}{2})$-approximation to the first-best benchmark for every prior.