Selfish Bin Packing

Epstein, Leah; Kleiman, Elena

doi:10.1007/978-3-540-87744-8_31

Cited by 15 publications

(37 citation statements)

References 22 publications

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“…A preliminary version of this paper appeared as [12]. Later, Yu and Zhang [32], independently, used a similar construction to prove a lower bound of the same value on the PoA, and claimed an upper bound of 1.6575 on the PoA.…”

Section: Our Results and Organization Of The Papermentioning

confidence: 97%

Selfish Bin Packing

Epstein

Kleiman

2009

Algorithmica

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Following recent interest in the study of computer science problems in a game theoretic setting, we consider the well known bin packing problem where the items are controlled by selfish agents. Each agent is charged with a cost according to the fraction of the used bin space its item requires. That is, the cost of the bin is split among the agents, proportionally to their sizes. Thus, the selfish agents prefer their items to be packed in a bin that is as full as possible. The social goal is to minimize the number of the bins used. The social cost in this case is therefore the number of bins used in the packing.A pure Nash equilibrium is a packing where no agent can obtain a smaller cost by unilaterally moving his item to a different bin, while other items remain in their original positions. A Strong Nash equilibrium is a packing where there exists no subset of agents, all agents in which can profit from jointly moving their items to different bins. We say that all agents in a subset profit from moving their items to different bins if all of them have a strictly smaller cost as a result of moving, while the other items remain in their positions.We measure the quality of the equilibria using the standard measures PoA and PoS that are defined as the worst case worst/best asymptotic ratio between the social cost of a (pure) Nash equilibrium and the cost of an optimal packing, respectively. We also consider the recently introduced measures SPoA and SPoS, that are defined similarly to the PoA and the PoS, but consider only Strong Nash equilibria.We give nearly tight lower and upper bounds of 1.6416 and 1.6428, respectively, on the PoA of the bin packing game, improving upon previous result by Bilò. We study the Strong Nash equilibria of the bin packing game, and show that a packing is a Strong Nash equilibrium iff it is produced by the Subset Sum algorithm for bin Algorithmica (2011) 60: 368-394 369 packing. This characterization implies that the SPoA of the bin packing game equals the approximation ratio of the Subset Sum algorithm, for which an almost tight bound is known. Moreover, the fact that any lower bound instance for the Subset Sum algorithm can be converted by a small modification of the item sizes to a lower bound instance on the SPoS, implies that in the bin packing game SPoA = SPoS. Finally, we address the issue of complexity of computing a Strong Nash packing and show that no polynomial time algorithm exists for finding Strong Nash equilibria, unless P = NP.

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Section: Our Results and Organization Of The Papermentioning

confidence: 97%

Selfish Bin Packing

Epstein

Kleiman

2009

Algorithmica

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“…The importance of studying scheduling and packing problems under a gametheoretical framework is by now very well established and widely acknowledged (see e.g. [26,11,28,1,17,7,14]). We attempt to add to this body of knowledge by considering the multidimensional variant.…”

Section: Motivation and Frameworkmentioning

confidence: 99%

Scheduling selfish jobs on multidimensional parallel machines

Epstein

Kleiman

2014

Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures

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We study the multidimensional vector scheduling problem with selfish jobs, both in non-cooperative and in cooperative versions. We show existence of assignments that are Nash, strong Nash, weakly and strictly Pareto optimal Nash equilibria in these settings. We improve upon the previous bounds on the price of anarchy for the non-cooperative case, and find tight bounds for every number of machines and dimension. For the cooperative case we provide tight bounds on the strong prices of anarchy and stability, as well as tight bounds on weakly and strictly Pareto optimal prices of anarchy and stability, for every number of machines and dimension.

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“…When allocation decisions belong to a finite set (e.g., when agent/task i may select a subset of a finite set of resources) resource allocation can be addressed within the context of submodular optimization problems, as in [16], and coordination games, as in [8]. Some examples include common-pool problems [18,8], bin-packing problems [11] and load-balancing problems [28]. In the presence of soft constraints, relevant payoff-based learning may also include the learning-automata dynamics for convergence to Nash equilibria in convex games of [25].…”

Section: Related Work and Contributionsmentioning

confidence: 99%

Measurement-based efficient resource allocation with demand-side adjustments

Chasparis

2019

Automatica

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The problem of efficient resource allocation has drawn significant attention in many scientific disciplines due to its direct societal benefits, such as energy savings. Traditional approaches in addressing online resource allocation problems neglect the potential benefit of feedback information available from the running tasks/loads as well as the potential flexibility of a task to adjust its operation/service-level in order to increase efficiency. The present paper builds upon recent developments in the area of bandwidth allocation in computing systems and proposes a generalized design approach for resource allocation when only performance measurements of the running tasks are available, possibly corrupted by noise. We demonstrate through analysis and simulations the potential of the proposed scheme in providing fair and efficient allocation of resources in a large class of resource allocation problems.

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Selfish Bin Packing

Cited by 15 publications

References 22 publications

Selfish Bin Packing

Selfish Bin Packing

Scheduling selfish jobs on multidimensional parallel machines

Measurement-based efficient resource allocation with demand-side adjustments

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