Analysis of Several Task-Scheduling Algorithms for a Model of Multiprogramming Computer Systems

Krause, K. L.; Shen, Vincent; Schwetman, Herb

doi:10.1145/321906.321917

Cited by 109 publications

(71 citation statements)

References 7 publications

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“…Bin packing with cardinality constraints (and regular, non-splittable items) was introduced and studied in an offline environment as early as in 1975 by Krause, Shen and Schwetman [12,13]. They showed that the performance guarantee of the well known First Fit algorithm is at most 2.7 − 12 5k .…”

Section: { A(i) Opt(i) |Opt(i) = N}mentioning

confidence: 99%

Approximation Schemes for Packing Splittable Items with Cardinality Constraints

2010

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We continue the study of bin packing with splittable items and cardinality constraints. In this problem, a set of items must be packed into as few bins as possible. Items may be split, but each bin may contain at most k (parts of) items, where k is some fixed constant. Complicating the problem further is the fact that items may be larger than 1, which is the size of a bin. We close this problem by providing a polynomial-time approximation scheme for it. We first present a scheme for the case k = 2 and then for the general case of constant k.Additionally, we present dual approximation schemes for k = 2 and constant k. Thus we show that for any ε > 0, it is possible to pack the items into the optimal number of bins in polynomial time, if the algorithm may use bins of size 1 + ε.

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Section: { A(i) Opt(i) |Opt(i) = N}mentioning

confidence: 99%

Approximation Schemes for Packing Splittable Items with Cardinality Constraints

2010

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“…Cardinality constrained bin packing was studied in the offline environment already in 1975 by Krause, Shen and Schwetman [12,13]. They showed that the performance guarantee of the well known First Fit algorithm is at most 2.7 − 12 5k .…”

Section: A(σ) Op T (σ)mentioning

confidence: 99%

Online Bin Packing with Cardinality Constraints

Epstein

2006

SIAM J. Discrete Math.

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We consider a one dimensional storage system where each container can store a bounded amount of capacity as well as a bounded number of items k ≥ 2. This defines the (standard) bin packing problem with cardinality constraints which is an important version of bin packing, introduced by Krause, Shen and Schwetman already in 1975. Following previous work on the unbounded space online problem, we establish the exact best competitive ratio for bounded space online algorithms for every value of k. This competitive ratio is a strictly increasing function of k which tends to Π ∞ + 1 ≈ 2.69103 for large k. Lee and Lee showed in 1985 that the best possible competitive ratio for online bounded space algorithms for the classical bin packing problem is the sum of a series, and tends to Π ∞ as the allowed space (number of open bins) tends to infinity. We further design optimal online bounded space algorithms for variable sized bin packing, where each allowed bin size may have a distinct cardinality constraint, and for the resource augmentation model. All algorithms achieve the exact best possible competitive ratio possible for the given problem, and use constant numbers of open bins. Finally, we introduce unbounded space online algorithms with smaller competitive ratios than the previously known best algorithms for small values of k, for the standard cardinality constrained problem. These are the first algorithms with competitive ratio below 2 for k = 4, 5, 6.

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“…This problem was studied also in [17,10,4]. Cardinality constrained bin packing was first studied by Krause, Shen and Schwetman [18,19]. It was also studied in [3,8].…”

Section: Introductionmentioning

confidence: 99%

Online Interval Coloring with Packing Constraints

Epstein

Levy

2005

Mathematical Foundations of Computer Science 2005

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Abstract. We study online interval coloring problems with bandwidth. We are interested in some variants motivated by bin packing problems. Specifically we consider open-end coloring, cardinality constrained coloring, coloring with vector constraints and finally a combination of both the cardinality and the vector constraints. We construct competitive algorithms for each of the variants. Additionally, we present a lower bound of 24/7 for interval coloring with bandwidth, which holds for all the above models, and improves the current lower bound for the standard interval coloring with bandwidth problem.

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Analysis of Several Task-Scheduling Algorithms for a Model of Multiprogramming Computer Systems

Cited by 109 publications

References 7 publications

Approximation Schemes for Packing Splittable Items with Cardinality Constraints

Approximation Schemes for Packing Splittable Items with Cardinality Constraints

Online Bin Packing with Cardinality Constraints

Online Interval Coloring with Packing Constraints

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