2010
DOI: 10.1007/s00453-010-9445-6
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Approximation Schemes for Packing Splittable Items with Cardinality Constraints

Abstract: 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… Show more

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Cited by 20 publications
(11 citation statements)
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“…While the problems differ slightly from ours, we see from several papers that their competitive ratio often ranges between 1.5 and 2 [8], [13], with the implication that allocating twice the number of machines would be sufficient. Yet, this is a high cost and we study below how it is possible to improve this limit in a practical case.…”
Section: Basic Modelcontrasting
confidence: 56%
See 1 more Smart Citation
“…While the problems differ slightly from ours, we see from several papers that their competitive ratio often ranges between 1.5 and 2 [8], [13], with the implication that allocating twice the number of machines would be sufficient. Yet, this is a high cost and we study below how it is possible to improve this limit in a practical case.…”
Section: Basic Modelcontrasting
confidence: 56%
“…In our case, this property is also extended to items of size smaller than bin size. It has been shown [8], [11] that this problem is NP-hard for any maximum number of item per bin-Max s m in our case. Bin packing problems appear in a number of variations.…”
Section: Basic Modelmentioning
confidence: 68%
“…They also show that the general case for k ≥ 3 is NP-hard and give an efficient 7 5 -approximation algorithm for k = 2. Finally, Epstein and van Stee [4] present polynomial-time approximation schemes for sublinear k.…”
Section: Related Work and Contributionmentioning
confidence: 99%
“…The behavior of algorithms on instances with relatively large optimal value can be evaluated by an asymptotic approximation ratio measure. For the definition of the above mentioned measures the readers are addressed to Section 8 in Vidar (2005) and to Epstein and van Stee (2008).…”
Section: An Ensemble Of Collaborating Algorithmsmentioning
confidence: 99%