cloud computing engineers

Abstract: We study the problem of characterizing the optimal consistency--robustness tradeoff for single-machine non-clairvoyant scheduling with predicted processing times. For a fixed number of jobs $n$, Wei and Zhang (2020) established a lower bound on the achievable consistency--robustness tradeoff which is known to be tight only in a few restrictive cases, leaving the optimal tradeoff for general $n$ unresolved. A different worst-case-$n$ regime was introduced by Benomar et al. (2025), who applied the former work's construction to show that for $λ\in (0, 1)$, any $(1+λ)$-consistent algorithm must be $1 + Ω(\sqrt{1/λ})$-robust. On the other hand, the best known upper bound gives $(1+λ)$-consistency and $1+O(1/λ)$-robustness, leaving a polynomial gap. In this work, we develop a new lower bound using a multi-stage adversarial construction and a new algorithm that together give a near-optimal characterization of the consistency--robustness tradeoff: for every $n$, our upper bound is within a multiplicative factor $3/2$ of our lower bound, and thus our algorithm is within a multiplicative factor $3/2$ of the online optimal. In particular, our lower bound shows that any $(1+λ)$-consistent algorithm must have robustness at least $1/\sqrtλ$ as $n \to \infty$, while our algorithm achieves robustness at most $\frac{1}{2}+\sqrt{\frac{5}{4}+1/λ}$ for any $n$, matching the lower bound in the leading term as $λ\downarrow 0$; our upper bound also closes the polynomial gap in the worst-case-$n$ regime. We additionally show how our algorithm can be made error-tolerant, preserving the near-optimal consistency-robustness tradeoff while incurring only slightly degraded performance under bounded prediction errors.

Abstract: In this paper we study consistent hashing (a.k.a. sparse partitions) for doubling metrics in the Massively Parallel Computation (MPC) model. A $(Γ,Λ)$-hash with diameter bound $Δ$ partitions a metric space into clusters of diameter at most $Δ$ such that every ball of radius $Δ/Γ$ intersects at most $Λ$ clusters in expectation. Consistent hashing has emerged as a central tool in geometric MPC algorithms. However, so far it has been solely used in Euclidean spaces, where it can be pre-computed. On the other hand, in cases where the metric space is received as input and unknown in advance, no previous parallel construction was known. We present the first fully scalable MPC algorithm over machines with local space $n^σ$, that given an $n$-point metric space with doubling dimension $d\leq O(σ\log n)$, samples a randomized $(Γ,2^{O(d/Γ)})$-hash in $O(d/σ^3)$ rounds. There is a dichotomy: if the doubling dimension is $d=Ω(σ\cdot\log n)$, a polynomial number of rounds is required to compute such a hash. We conclude by showing that this MPC primitive yields $O(d/σ^3)$-round fully scalable MPC algorithms for a broad class of fundamental geometric problems in doubling metrics, including stochastic tree embeddings with $O(\log n)$ expected distortion, constant factor approximation for facility location, bicriteria $(O(ε^{-2}),1+ε)$-approximation for $k$-median and $k$-means.