Approximate strip packing

Kenyon, Claire; Rémila, Éric

doi:10.1109/sfcs.1996.548461

Cited by 56 publications

(44 citation statements)

References 8 publications

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“…Some problems closely related to job scheduling in smart grid include link scheduling in wireless networks [22], [32], [36], parallel job scheduling [34], [11], [27], [10], [12] rectangle packing [13], [19], [20], [26] and Orthogonal Rectangular Strip Packing Problem (SPP) [2], [14], [17], [24], sometimes also called orthogonal packing in two dimensions. Essentially, the goal is to find the best orthogonal placement of a set of rectangles on a strip of rectangular stock sheet with a fixed width and infinite height.…”

Section: Related Workmentioning

confidence: 99%

Smoothing the energy consumption: Peak demand reduction in smart grid

Tang

Huang

et al. 2013

2013 Proceedings IEEE INFOCOM

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Abstract-Assume that a set of Demand Response Switch (DRS) devices are deployed in smart meters for autonomous demand side management within one house. The DRS devices are able to sense and control the activity of each appliance. We propose a set of appliance scheduling algorithms to 1) minimize the peak power consumption under a fixed delay requirement, and 2) minimize the delay under a fixed peak demand constraint. For both problems, we first prove that they are NP-Hard. Then we propose a set of approximation algorithms with constant approximation ratios. We conduct extensive simulations using both real-life appliance energy consumption data trace and synthetic data to evaluate the performance of our algorithms. Extensive evaluations verify that the schedules obtained by our methods significantly reduce the peak demand or delay compared with naive greedy algorithm or randomized algorithm.

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Section: Related Workmentioning

confidence: 99%

Smoothing the energy consumption: Peak demand reduction in smart grid

Tang

Huang

et al. 2013

2013 Proceedings IEEE INFOCOM

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“…2) Approximation algorithms: Approximation algorithms exist [4], [12] that are able to find solutions within´½ · µ of optimal in time that is polynomial in the number of rectangles but exponential in other variables. Unfortunately, for our problem sizes, we believe that no point along the runtime-vs.-¯tradeoff will be acceptable (too much error is introduced and runtime remains high).…”

Section: ) Exhaustive Searchmentioning

confidence: 99%

Co-scheduling of Disk Head Time in Cluster-Based Storage

Wachs

Ganger

2009

2009 28th IEEE International Symposium on Reliable Distributed Systems

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Abstract-Disk timeslicing is a promising technique for storage performance insulation. To work with cluster-based storage, however, timeslices associated with striped data must be co-scheduled on the corresponding servers. This paper describes algorithms for determining global timeslice schedules and mechanisms for coordinating the independent server activities. Experiments with a prototype show that, combined, they can provide performance insulation for workloads sharing a storage cluster -each workload realizes a configured minimum efficiency within its timeslices regardless of the activities of the other workloads.

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“…We believe that this approach for rounding and assignment of suitable items will find other applications in related packing or scheduling problems. Furthermore, we use techniques like dual approximation [8], partition of the instance, linear grouping and rounding known from Bin Packing [6] or Strip Packing [17,18], and definition of configurations. Our modelization also involves the multiple subset sum problem (MSSP) which can be formally defined as follows.…”

Section: Introductionmentioning

confidence: 99%

Improved Approximation Algorithms for Scheduling with Fixed Jobs

Diedrich¹,

Jansen²

2009

Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms

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We study two closely related problems in non-preemptive scheduling of sequential jobs on identical parallel machines. In these two settings there are either fixed jobs or nonavailability intervals during which the machines are not available; in either case, the objective is to minimize the makespan. Both formulations have different applications, e.g. in turnaround scheduling or overlay computing. For both problems we contribute approximation algorithms with an improved ratio of 3/2 + , respectively. For scheduling with fixed jobs, a lower bound of 3/2 on the approximation ratio has been obtained by Scharbrodt, Steger & Weisser; for scheduling with non-availability we provide the same lower bound. In total, our approximation ratio for both problems is essentially tight via suitable inapproximability results. We use dual approximation, creation of a gap structure and job configurations, and a PTAS for the multiple subset sum problem. However, the main feature of our algorithms is a new technique for the assignment of large jobs via flexible rounding. Our new technique is based on an interesting cyclic shifting argument in combination with a network flow model for the assignment of jobs to large gaps.

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Approximate strip packing

Cited by 56 publications

References 8 publications

Smoothing the energy consumption: Peak demand reduction in smart grid

Smoothing the energy consumption: Peak demand reduction in smart grid

Co-scheduling of Disk Head Time in Cluster-Based Storage

Improved Approximation Algorithms for Scheduling with Fixed Jobs

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