Approximate algorithms to pack rectangles into several strips

Zhuk, Sergey

doi:10.1515/156939206776241264

Cited by 34 publications

(15 citation statements)

References 7 publications

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“…It corresponds to packing a set of rectangles (without rotations and overlaps) into a strip of machines in order to minimize the height used. Then, this problem was extended to the case where the rectangles were packed into a finite number of strips [3,4]. More recently, an asymptotic (1+ )-approximation AFPTAS with additive constant O(1) and with running-time polynomial in n and in 1/ was presented in [5].…”

Section: Related Workmentioning

confidence: 99%

Multi‐organization scheduling approximation algorithms

Cohen¹,

Cordeiro²,

Trystram³

et al. 2011

Concurrency and Computation

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SUMMARYIn this paper we consider the problem of scheduling on computing platforms composed of several independent organizations, known as the Multi-Organization Scheduling Problem (MOSP). Each organization provides both resources and jobs and follows its own objectives. We are interested in the best way to minimize the makespan on the entire platform when the organizations behave in a selfish way. We study the complexity of the MOSP problem with two different local objectives-makespan and average completion time-and show that MOSP is strongly NP-Hard in both cases. We formally define a selfishness notion, by means of restrictions on the schedules. We prove that selfish behavior imposes a lower bound of 2 on the approximation ratio for the global makespan. We present various approximation algorithms of ratio 2 which validate selfishness restrictions. These algorithms are experimentally evaluated through simulation, exhibiting good average performances and presenting good fairness to organizations' local objectives.

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Section: Related Workmentioning

confidence: 99%

Multi‐organization scheduling approximation algorithms

Cohen¹,

Cordeiro²,

Trystram³

et al. 2011

Concurrency and Computation

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show abstract

“…Strip packing was extended to the case where the rectangles must be packed into a finite number of strips [2], [3]. Recently, Jansen et al [4] presented an asymptotic (1 + )-approximation AFPTAS with additive constant O(1) and with running-time polynomial in n and in 1/ .…”

Section: B Related Workmentioning

confidence: 99%

“…To achieve a makespan of 1, the jobs of organizations O (2) and O (3) must be scheduled together. In the best case, the job of O (2) is scheduled before the job of O (3) which leads to an approximation ratio of ( 3 2 ; 1).…”

Section: A Principlementioning

confidence: 99%

“…In the best case, the job of O (2) is scheduled before the job of O (3) which leads to an approximation ratio of ( 3 2 ; 1). This means that if the approximation ratio for the global makespan is bounded by 1, then no algorithm can construct a solution with a degree of cooperativeness better than 3 2 (see Figure 2(a)).…”

Section: A Principlementioning

confidence: 99%

“…This means that if the approximation ratio for the global makespan is bounded by 1, then no algorithm can construct a solution with a degree of cooperativeness better than 3 2 (see Figure 2(a)). On the other hand, if the schedule targets to achieve C max < 2 and a degree of cooperativeness α = 1, then the jobs of O (2) and O (3) must start at time 0. Starting the first job of O (1) at time 0, the second one can start as soon as the job of organization O (2) finishes.…”

Section: A Principlementioning

confidence: 99%

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Tight Analysis of Relaxed Multi-organization Scheduling Algorithms

Cordeiro

Dutot

Mounié

et al. 2011

2011 IEEE International Parallel &Amp; Distributed Processing Symposium

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Abstract-The goal of this paper is to study how limited cooperation can impact the quality of the schedule obtained by multiple independent organizations in a typical grid computing platform. This relaxed version of the problem known as the Multi-Organization Scheduling Problem (MOSP) models an environment where organizations providing both resources and jobs tolerate a bounded degradation on the makespan of their own jobs in order to minimize the makespan over the entire platform.More precisely, the technical contributions are the following. First, we improve the existing inapproximation bounds for this problem proving that what was previously though as not polynomially approximable (unless P = N P ) is actually not approximable at all. We achieve this using two families of instances whose Pareto optimal solutions are on par with the previous inaproximability bounds.Then, we present two algorithms that solve the problem with approximation ratios of (2; 3/2) and (3; 4/3) respectively. This means that when using the first (second) algorithm, if an organization tolerates that the completion time of its last job cannot exceed twice (three times) the time it would have obtained by itself, then the algorithm provides a solution that is a 3/2-approximation (4/3-approximation) for the optimal global makespan. Both algorithms are efficient since their performance ratio correspond to the Pareto optimal solutions of the previously defined instances.

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Coordination mechanisms for decentralized parallel systems

Cohen

Cordeiro

Trystram

2014

Concurrency and Computation

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International audienceOn resource sharing platforms, the execution of the jobs submitted by users is usually controlled by a centralized global scheduler. It determines efficient schedules regarding some common objective function that all organizations agree with (for instance, maximizing the utilization of the entire platform). However, in practice, each organization is mostly interested in the performance obtained for its own jobs. We study the price that the collectivity must pay in order to allow independence to selfish, self-governing organizations, so they can choose the best schedules for their own jobs. In other words, we are interested in analyzing the costs on the global performance inflicted by the decentralization of scheduling policies. We present a game-theoretic model for the problem and the associated coordination mechanisms developed to reduce the cost of the decentralization of the decision-making process. The main contribution is to show (in theory and practice) how to devise pure Nash equilibria configurations for every instance of the problem and to prove that the price paid by the collectivity depends on the local scheduling policy and on the characteristics of the workload executed on such platform

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Approximate algorithms to pack rectangles into several strips

Cited by 34 publications

References 7 publications

Multi‐organization scheduling approximation algorithms

Multi‐organization scheduling approximation algorithms

Tight Analysis of Relaxed Multi-organization Scheduling Algorithms

Coordination mechanisms for decentralized parallel systems

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