Random redundant storage in disk arrays: Complexity of retrieval problems

Aerts, J.; Korst, Jan; Spieksma, Frits; Verhaegh, Wfj Wim; Woeginger, Gerhard J.

doi:10.1109/tc.2003.1228515

Cited by 5 publications

(4 citation statements)

References 22 publications

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“…|M j | = 2 for all j. However, for that case we can prove by a reduction from a special form of satisÿability [17] that the problem remains NP-complete in the strong sense [13].…”

Section: Time-based Load Balancingmentioning

confidence: 96%

“…We use the fact that all arcs, except for the arcs from the source and the arcs to the sink, are directed from the edge nodes to the disk nodes and that the maximum ow is at most n, such that an algorithm for BRP can be constructed with a time complexity of O(mn log n) [13], where the log n part comes from a bisection search over values of K.…”

Section: Block-based Load Balancingmentioning

confidence: 99%

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Load balancing for redundant storage strategies: Multiprocessor scheduling with machine eligibility

2001

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An important cost issue in multimedia servers is disk load balancing, such that the available hard disks are used as e ciently as possible. Disk load balancing is often done on a block basis, but can also be done on a time basis, by taking into account the actual transfer times of the blocks. In the latter approach we can also embed the disk switch times. In this paper we revisit block-based load balancing and introduce time-based load balancing. For each approach we present a mathematical model and analyse the complexity of the corresponding retrieval problem. We give algorithms with a performance bound for the NP-hard time-based retrieval problem and use simulation to compare the results of these algorithms with a maximum ow algorithm for the block-based retrieval problem.

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“…|M j | = 2 for all j. However, for that case we can prove by a reduction from a special form of satisÿability [17] that the problem remains NP-complete in the strong sense [13].…”

Section: Time-based Load Balancingmentioning

confidence: 96%

Section: Block-based Load Balancingmentioning

confidence: 99%

Load balancing for redundant storage strategies: Multiprocessor scheduling with machine eligibility

2001

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“…The proof is by reduction from the strongly NP-hard scheduling problem P |M j |C max ≤ 2 [3]. According to the notation for machine scheduling problems [4], problem P |M j |C max ≤ 2 can be described as follows.…”

Section: Problem Complexitymentioning

confidence: 99%

Radio resource allocation in OFDMA multi-cell networks

Detti¹,

Moretti²,

Abrardo³

2010

Preprint

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In this paper, the problem of allocating users to radio resources (i.e., subcarriers) in the downlink of an OFDMA cellular network is addressed. We consider a multi-cellular environment with a realistic interference model and a margin adaptive approach, i.e., we aim at minimizing total transmission power while maintaining a certain given rate for each user. The computational complexity issues of the resulting model is discussed and proving that the problem is NP-hard in the strong sense. Heuristic approaches, based on network flow models, that finds optima under suitable conditions, or "reasonably good" solutions in the general case are presented. Computational experiences show that, in a comparison with a commercial state-of-the-art optimization solver, the proposed algorithms are effective in terms of solution quality and CPU times.

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“…Dawande et al [4] showed a combinatorial 2-approximation algorithm for the restricted case of the MK-AR where the size of an item is equal to its profit. Approximation algorithms for other restricted instances of the MK-AR have been studied as well [1,2].…”

Section: Introductionmentioning

confidence: 99%

Approximability of Two Variants of Multiple Knapsack Problems

Miyazaki

Morimoto

Okabe

2015

Lecture Notes in Computer Science

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This paper considers two variants of Multiple Knapsack Problems. The first one is the Multiple Knapsack Problem with Assignment Restrictions and Capacity Constraints (MK-AR-CC). In the MK-AR-CC(k) (where k is a positive integer), a subset of knapsacks is associated with each item and the item can be packed into only those knapsacks (Assignment Restrictions). Furthermore, the size of each knapsack is at least k times the largest item assignable to the knapsack (Capacity Constraints). The MK-AR-CC(k) is NP-hard for any constant k. In this paper, we give a polynomial-time " 1 + 2 k+1 + "-approximation algorithm for the MK-AR-CC(k), and give a lower bound on the approximation ratio of our algorithm by showing an integrality gap of`1 + 1 k − ´f or the IP formulation we use in our algorithm, where is an arbitrary small positive constant. The second problem is the Splittable Multiple Knapsack Problem with Assignment Restrictions (S-MK-AR), in which the size of items may exceed the capacity of knapsacks and items can be split and packed into multiple knapsacks. We show that approximating the S-MK-AR with the ratio of n 1− is NP-hard even when all the items have the same profit, where n is the number of items and is an arbitrary positive constant.

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Random redundant storage in disk arrays: Complexity of retrieval problems

Cited by 5 publications

References 22 publications

Load balancing for redundant storage strategies: Multiprocessor scheduling with machine eligibility

Load balancing for redundant storage strategies: Multiprocessor scheduling with machine eligibility

Radio resource allocation in OFDMA multi-cell networks

Approximability of Two Variants of Multiple Knapsack Problems

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