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This article presentsuniversalalgorithms for clustering problems, including the widely studiedk-median,k-means, andk-center objectives. The input is a metric space containing allpotentialclient locations. The algorithm must selectkcluster centers such that they are a good solution foranysubset of clients that actually realize. Specifically, we aim for lowregret, defined as the maximum over all subsets of the difference between the cost of the algorithm’s solution and that of an optimal solution. A universal algorithm’s solutionSolfor a clustering problem is said to be an α , β-approximation if for all subsets of clientsC′, it satisfiessol(C′) ≤ α ċopt(C′) + β ċmr, whereopt(C′ is the cost of the optimal solution for clients (C′) andmris the minimum regret achievable by any solution. Our main results are universal algorithms for the standard clustering objectives ofk-median,k-means, andk-center that achieve (O(1),O(1))-approximations. These results are obtained via a novel framework for universal algorithms using linear programming (LP) relaxations. These results generalize to other ℓp-objectives and the setting where some subset of the clients arefixed. We also give hardness results showing that (α, β)-approximation is NP-hard if α or β is at most a certain constant, even for the widely studied special case of Euclidean metric spaces. This shows that in some sense, (O(1),O(1))-approximation is the strongest type of guarantee obtainable for universal clustering.
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This content will become publicly available on May 27, 2026
Online Fair Allocation of Reusable Resources
Motivated by the emerging paradigm of resource allocation that integrates classical objectives, such as cost minimization, with societal objectives, such as carbon awareness, this paper proposes a general framework for the online fair allocation of reusable resources. Within this framework, an online decision-maker seeks to allocate a finite resource with capacityCto a sequence of requests arriving with unknown distributions of types, utilities, and resource usage durations. To accommodate diverse objectives, the framework supports multiple actions and utility types, and the goal is to achieve max-min fairness among utilities, i.e., maximize the minimum time-averaged utility across all utility types. Our performance metric is an (α,β)-competitive guarantee of the form: ALG ≥ α • OPT*- O(Tβ-1),; α, β ∈ (0, 1], where OPT*and ALG are the time-averaged optimum and objective value achieved by the decision maker, respectively. We propose a novel algorithm that achieves a competitive guarantee of (1-O(√(log C/C)), 2/3) under the bandit feedback. As resource capacity increases, the multiplicative competitive ratio term 1-O(√ logC/C) asymptotically approaches optimality. Notably, when the resource capacity exceeds a certain threshold, our algorithm achieves an improved competitive guarantee of (1, 2/3). Our algorithm employs an optimistic penalty-weight mechanism coupled with a dual exploration-discarding strategy to balance resource feasibility, exploration, and fairness among utilities.
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- PAR ID:
- 10655793
- Publisher / Repository:
- ACM
- Date Published:
- Journal Name:
- Proceedings of the ACM on Measurement and Analysis of Computing Systems
- Volume:
- 9
- Issue:
- 2
- ISSN:
- 2476-1249
- Page Range / eLocation ID:
- 1 to 46
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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