Approximating the Non-contiguous Multiple Organization Packing Problem

Bougeret, Marin; Dutot, Pierre Francois; Jansen, Klaus; Otte, Christina; Trystram, Denis

doi:10.1007/978-3-642-15240-5_23

Cited by 13 publications

(20 citation statements)

References 12 publications

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“…Bougeret et al [6] improved the result to a 2-approximation and also presented an AFPTAS. Recently, Bougeret et al [5,4] designed 5/2-approximation algorithms for identical and heterogeneous platforms.…”

Section: Related Workmentioning

confidence: 99%

Coordination Mechanisms for Selfish Parallel Jobs Scheduling

Zhang

2012

Lecture Notes in Computer Science

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Abstract.A set of parallel jobs must be scheduled in a grid, which has multi clusters that consist of many identical processors, to minimize the global objective function, the makespan. A parallel job requires several processors for simultaneously executing and it needs some unit times to finish its execution. In practice, each parallel job is owned by an independent agent, which is selfish and select a cluster to minimize its own completion time. This scenario can be represented as a coordination mechanism game, in which the players are job owners, and the strategies are the clusters, and the player's disutility is the completion time of its job in the corresponding schedule.In this work, we design and analyze coordination mechanisms for machines, which aim to minimize the price of anarchy. We study two classes of scheduling policies, the Bottom-Left based algorithms and the ShelfPacking based algorithms, both in a homogeneous grid and in a heterogeneous grid. We derive upper and lower bounds on the price of anarchy of these coordination mechanisms. We also show that such games are potential games that converge in a linear number of rounds.

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Section: Related Workmentioning

confidence: 99%

Coordination Mechanisms for Selfish Parallel Jobs Scheduling

Zhang

2012

Lecture Notes in Computer Science

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“…In this paper, we recall the methodology that formalizes the common principles used in [1,2], and we apply it to get a new 7 3 -approximation for MCSP running in O(log(nh max )N(n + log(n))), which is clearly faster than the previous mentioned algorithms.…”

Section: Motivations and Contributionsmentioning

confidence: 99%

“…We must distinguish the 3-approximation in [5] and the 5 2 -approximation in [1] that have a low cost from the costly 2-approximation in [6] and 2 + -approximation in [7].…”

Section: Related Workmentioning

confidence: 99%

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Improved approximation algorithms for scheduling parallel jobs on identical clusters

Bougeret

Dutot

Trystram

et al. 2015

Theoretical Computer Science

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The Multiple Cluster Scheduling Problem corresponds to minimizing the maximum completion time (makespan) of a set of n parallel rigid (and non-preemptive) jobs submitted to N identical clusters. It cannot be approximated with a ratio better than 2 (unless P = N P). We present in this paper the methodology that encompasses several existing results [1,2]. We detail first how to apply it for obtaining a 5 2 -approximation. Then, we use it to provide a new 7 3 -approximation running in O(log(nh max )N(n + log(n))), where h max is the processing time of the longest job. Finally, we apply it to a restriction of the problem to jobs of limited size, leading to a 2-approximation which is the best possible ratio since the restriction remains 2-inapproximable.

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“…Related Results: Strip packing with slicing has been studied for a variant in which the width of each rectangle represents a demand for a number of concurrently running processors [2]. However, this problem differs substantially from 2SP-S because the slices must have integer widths and must be horizontally aligned due to concurrency, and results for it do not carry over.…”

Section: Introductionmentioning

confidence: 99%

Smart-Grid Electricity Allocation via Strip Packing with Slicing

Alamdari

Biedl

Chan

et al. 2013

Lecture Notes in Computer Science

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Abstract. One advantage of smart grids is that they can reduce the peak load by distributing electricity-demands over multiple short intervals. Finding a schedule that minimizes the peak load corresponds to a variant of a strip packing problem. Normally, for strip packing problems, a given set of axis-aligned rectangles must be packed into a fixed-width strip, and the goal is to minimize the height of the strip. The electricityallocation application can be modelled as strip packing with slicing: each rectangle may be cut vertically into multiple slices and the slices may be packed into the strip as individual pieces. The stacking constraint forbids solutions in which a vertical line intersects two slices of the same rectangle. We give a fully polynomial time approximation scheme for this problem, as well as a practical polynomial time algorithm that slices each rectangle at most once and yields a solution of height at most 5/3 times the optimal height.

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Approximating the Non-contiguous Multiple Organization Packing Problem

Cited by 13 publications

References 12 publications

Coordination Mechanisms for Selfish Parallel Jobs Scheduling

Coordination Mechanisms for Selfish Parallel Jobs Scheduling

Improved approximation algorithms for scheduling parallel jobs on identical clusters

Smart-Grid Electricity Allocation via Strip Packing with Slicing

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