Bin Packing Approximation Algorithms: Survey and Classification

Coffman, E. G.; Csirik, János; Galambos, Gábor; Martello, Silvano; Vigo, Daniele

doi:10.1007/978-1-4419-7997-1_35

Cited by 221 publications

(175 citation statements)

References 134 publications

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“…The online bin packing problem has many applications in practice, from cutting stock applications to creating file backups in removable media [15,16]. Heuristics that have been proposed for the problem include Next-Fit (Nf), First-Fit (Ff), Best-Fit (Bf), and the Harmonic-based class of algorithms.…”

Section: Introductionmentioning

confidence: 99%

Online Bin Packing with Advice

et al. 2014

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We consider the online bin packing problem under the advice complexity model where the "online constraint" is relaxed and an algorithm receives partial information about the future items. We provide tight upper and lower bounds for the amount of advice an algorithm needs to achieve an optimal packing. We also introduce an algorithm that, when provided with log n+o(log n) bits of advice, achieves a competitive ratio of 3/2 for the general problem. This algorithm is simple and is expected to find real-world applications. We introduce another algorithm that receives 2n + o(n) bits of advice and achieves a competitive ratio of 4/3 + ε. Finally, we provide a lower bound argument that implies that advice of linear size is required for an algorithm to achieve a competitive ratio better than 9/8.

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Section: Introductionmentioning

confidence: 99%

Online Bin Packing with Advice

et al. 2014

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“…Bin packing is a classical combinatorial optimization problem [6,8,9]. The objective is to pack a set of items into a minimum number of unit-size bins such that the total size of the items in a bin does not exceed the bin capacity.…”

Section: Introductionmentioning

confidence: 99%

An 8/3 Lower Bound for Online Dynamic Bin Packing

Wong

Yung

Burcea

2012

Algorithms and Computation

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Abstract. We study the dynamic bin packing problem introduced by Coffman, Garey and Johnson. This problem is a generalization of the bin packing problem in which items may arrive and depart dynamically. The objective is to minimize the maximum number of bins used over all time. The main result is a lower bound of 8/3 ∼ 2.666 on the achievable competitive ratio, improving the best known 2.5 lower bound. The previous lower bounds were 2.388, 2.428, and 2.5. This moves a big step forward to close the gap between the lower bound and the upper bound, which currently stands at 2.788. The gap is reduced by about 60% from 0.288 to 0.122. The improvement stems from an adversarial sequence that forces an online algorithm A to open 2s bins with items having a total size of s only and this can be adapted appropriately regardless of the current load of other bins that have already been opened by A. Comparing with the previous 2.5 lower bound, this basic step gives a better way to derive the complete adversary and a better use of items of slightly different sizes leading to a tighter lower bound. Furthermore, we show that the 2.5-lower bound can be obtained using this basic step in a much simpler way without case analysis.

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“…Coffman and Csirik [73] also proposed a four-field classification scheme for papers on bin packing, aimed at highlighting the results in bin packing theory to be found in a certain article. More recently, Coffman et al [75] presented an overview of approximation algorithms for the BPP and a number of its variants, and classified all references according to [73].…”

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confidence: 99%

“…The most recent survey (2013), by Coffman et al [75], examines 200 references from the literature. Among the papers that appeared subsequently, we mention those by Dósa et al [106] on the FFD algorithm, by Rothvoß [242], who improved a classical result by Karmarkar and Karp [169], and by Balogh et al [21], who closed a long standing open issue on on-line bin packing.…”

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confidence: 99%