On Two Class-Constrained Versions of the Multiple Knapsack Problem

Shachnai, Hadas; Tamir, Tami

doi:10.1007/s004530010057

Cited by 79 publications

(69 citation statements)

References 25 publications

(24 reference statements)

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“…Placement problems have also been studied in the optimization literature, including bin packing, multiple knapsack, and multi-dimensional knapsack problems [11]. The special case of our problem with uniform memory requirements was studied in [12], and some approximation algorithms were proposed. The optimization problem that we consider presents a nonlinear optimization objective while previous approaches [8], [4] to the same problem use linear optimization objectives.…”

Section: Related Workmentioning

confidence: 99%

Utility-based placement of dynamic Web applications with fairness goals

Carrera

Steinder

Whalley

et al. 2008

NOMS 2008 - 2008 IEEE Network Operations and Management Symposium

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Abstract-We study the problem of dynamic resource allocation to clustered Web applications. We extend application server middleware with the ability to automatically decide the size of application clusters and their placement on physical machines. Unlike existing solutions, which focus on maximizing resource utilization and may unfairly treat some applications, the approach introduced in this paper considers the satisfaction of each application with a particular resource allocation and attempts to at least equally satisfy all applications. We model satisfaction using utility functions, mapping CPU resource allocation to the performance of an application relative to its objective. The demonstrated online placement technique aims at equalizing the utility value across all applications while also satisfying operational constraints, preventing the over-allocation of memory, and minimizing the number of placement changes. We have implemented our technique in a leading commercial middleware product. Using this real-life testbed and a simulation we demonstrate the benefit of the utility-driven technique as compared to other state-of-the-art techniques.

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Section: Related Workmentioning

confidence: 99%

Utility-based placement of dynamic Web applications with fairness goals

Carrera

Steinder

Whalley

et al. 2008

NOMS 2008 - 2008 IEEE Network Operations and Management Symposium

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“…Other related works deal with a special case of the class-constrained multiple knapsack (CCMK) problem [17], [18], in which a set of unit-sized items of m different types (u i items of type i) need to be placed in n bins; each bin has a limited capacity, t j , and a bound, a j , on the number of distinct types of items it can hold. The objective is to pack as many items as possible in the bins.…”

Section: Related Workmentioning

confidence: 99%

“…The objective is to pack as many items as possible in the bins. The application of this problem to data placement on parallel disks was studied in [18] and [8]. When each knapsack is represented by a job with length t j and allotment parameter a j , and the items of type i are represented by a machine, M i , with rate u i , we get an instance of the SAC problem.…”

Section: Related Workmentioning

confidence: 99%

Multiprocessor Scheduling with Machine Allotment and Parallelism Constraints

Shachnai

Tamir

2002

Algorithmica

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Abstract. Modern computer systems distribute computation among several machines to speed up the execution of programs. Yet, setup and communication costs, as well as parallelism constraints, bound the number of machines that can share the execution of a given application, and the number of machines by which it can be processed simultaneously. We study the resulting scheduling problem, stated as follows. Given a set of n jobs and m uniform machines, assign the jobs to the machines subject to parallelism and machine allotment constraints, such that the overall completion time of the schedule (or makespan) is minimized. Indeed, the multiprocessor scheduling problem (where each job can be processed by a single machine) is a special case of our problem; thus, our problem is strongly NP-hard.We present a (1 + α)-approximation algorithm for this problem, where α ∈ (0, 1] depends on the minimal number of machine allotments and the minimal parallelism allowed for any job. Also, we show that when the maximal number of machines that can share the execution of a job is some fixed constant, our problem has a polynomial time approximation scheme; for other special cases we give optimal polynomial time algorithms. Finally, through the relation of our problem to the classic preemptive scheduling problem on multiple machines, we shed some fresh light on what is known in scheduling folklore as the power of preemption.

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“…For the online version, Krumke et al [15] show that the competitive ratio of GreedyFit is at least 2m, the competitive ratio of OneBin is at most 2m − 1, and that the competitive ratio of any randomized algorithm is Ω(m) even if it is allowed to use more than m bins simultaneously. The Bin Coloring problem is also related to class-contrained knapsack problems [23,24]. In those versions of the knapsack problem, each item is characterized by a size and a color and each knapsack has an additional limit on the number of different colors that it can hold.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Analysis of Online Bin Coloring Algorithms Via Stochastic Comparison

Hiller

Vredeveld

2008

Algorithms - ESA 2008

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This paper proposes a new method for probabilistic analysis of online algorithms that is based on the notion of stochastic dominance. We develop the method for the Online Bin Coloring problem introduced in [15]. Using methods for the stochastic comparison of Markov chains we establish the strong result that the performance of the online algorithm GreedyFit is stochastically dominated by the performance of the algorithm OneBin for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations.

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On Two Class-Constrained Versions of the Multiple Knapsack Problem

Cited by 79 publications

References 25 publications

Utility-based placement of dynamic Web applications with fairness goals

Utility-based placement of dynamic Web applications with fairness goals

Multiprocessor Scheduling with Machine Allotment and Parallelism Constraints

Probabilistic Analysis of Online Bin Coloring Algorithms Via Stochastic Comparison

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