SearcharxivSearch

arXiv · 2507.08846

Precomputed Dominant Resource Fairness

Abstract

Although resource allocation is a well studied problem in computer science, until the prevalence of distributed systems, such as computing clouds and data centres, the question had been addressed predominantly for single resource type scenarios. At the beginning of the last decade, with the introuction of Dominant Resource Fairness, the studies of the resource allocation problem has finally extended to the multiple resource type scenarios. Dominant Resource Fairness is a solution, addressing the problem of fair allocation of multiple resource types, among users with heterogeneous demands. Based on Max-min Fairness, which is a well established algorithm in the literature for allocating resources in the single resource type scenarios, Dominant Resource Fairness generalises the scheme to the multiple resource case. It has a number of desirable properties that makes it preferable over alternatives, such as Sharing Incentive, Envy-Freeness, Pareto Efficiency, and Strategy Proofness, and as such, it is widely adopted in distributed systems. In the present study, we revisit the original study, and analyse the structure of the algorithm in closer view, to come up with an alternative algorithm, which approximates the Dominant Resource Fairness allocation in fewer steps. We name the new algorithm Precomputed Dominant Resource Fairness, after its main working principle.

Explore related subjects

Keep this discovery

BibTeXRIS

Serdar Metin. 2025-07-08. Precomputed Dominant Resource Fairness. https://arxiv.org/abs/2507.08846

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

MMS Allocation for Chores with Online Agent Arrivals

We study the fair allocation of $m$ indivisible chores to $n$ agents with subadditive cost functions arriving online in an arbitrary order. Upon an agent's arrival, we are informed of her cost function and must irrevocably assign her a set of chores. We focus on the Maximin Share (MMS) fairness notion and aim to compute an allocation in which all items are assigned, and no agent incurs a cost more than $\alpha$ times her MMS. Without any prior information about the instance (other than $n$ and $m$), we design an algorithm with a competitive ratio of $O(\min\{n, k\log^{1+\epsilon}k, \log m\})$ for any constant $\epsilon > 0$, where $k$ denotes the number of cost function types. Our bound matches the best known offline approximation guarantees for MMS under subadditive costs and is nearly optimal with respect to all three parameters: we show that even for binary additive cost functions, no online algorithm can achieve a competitive ratio of $o(\min\{n, k\log k, \log m\})$. We then consider the setting in which the $k$ cost function types are known in advance (though the realized types of arriving agents are not). For additive cost functions, we provide an algorithm with a competitive ratio of $O(\min\{\log k, \log(kn)/\log\log(kn)\})$, and show that constant-competitive algorithms do not exist for general $k$, even for the binary additive setting. For binary additive functions when $k \le n$, we propose a $3$-competitive algorithm and establish a lower bound of $2$.

cs.GT

Truncated Noisy Best-Response Algorithms: Toward Game Theoretic Learning with Safety Guarantees

We consider a game theoretic approach to solve multi-agent coordination problems with submodular maximization objectives. It is known for such problems that the Nash equilibria for the corresponding game are always within 50% of the optimal, but that the equilibria which achieve this worst-case bound are not stable. To exploit this instability, we propose a family of algorithms which we call Truncated Noisy Best-Response (TNBR) Algorithms. These algorithms are flexibly characterized by agents asynchronously and stochastically selecting actions from a neighbourhood of their best response payoffs. We compute bounds on the recurrent classes of TNBR algorithms' associated Markov chains. Our bounds fall into two categories: first, "Performance" bounds ensure that TNBR algorithms always have a high-value recurrent state; second, "Safety" bounds ensure that TNBR algorithms never have arbitrarily-bad recurrent states. Furthermore, these two types of bounds are linked by a waterbed-like effect: every game with a poor Safety guarantee necessarily has a favorable Performance guarantee.

cs.GT

Existence of the Core in Approval-Based Committee Elections

We settle the main open question in the theory of approval-based multi-winner elections: we show that there always exists a committee in the core. The core is a stability and group fairness concept. The proof introduces a new voting rule that optimizes an entropy-like objective function over committees and payment systems. All local optima of this objective function lie in the core, which implies that a core committee can be found in polynomial time.

cs.GT