On online bin packing with LIB constraints

Epstein, Leah

doi:10.1002/nav.20383

Cited by 13 publications

(9 citation statements)

References 9 publications

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“…A special case is investigated by Balogh et al [1], when there are only two colors, black and white, and they have shown a lower bound about 1.7213 on the asymptotic competitive ratio for any online algorithm. There is a model which is more similar to the one discussed in this work, than the above ones, this is the Bin Packing Problem with LIB ('Largest In Bottom') constraints, which has been also investigated by several authors [10,9,16,17]. This additional constraint means that one cannot put an item on another one with smaller size.…”

Section: A Bódismentioning

confidence: 83%

“…This additional constraint means that one cannot put an item on another one with smaller size. Epstein [10] proved that First-Fit gives not better than 2.5 competitive for the online case, which was improved by Dósa et al [9] to about 2.1666, and they also mentioned a model of Generalized LIB constraint, where the constraint is defined by an undirected incompatibility graph based on the sizes of the items, and adjacent items cannot be packed into the same bin.…”

Section: A Bódismentioning

confidence: 98%

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Bin packing with directed stackability conflicts

Bódis

2015

Acta Universitatis Sapientiae, Informatica

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The Bin Packing problem is a well-known and highly investigated problem in the computer science: we have n items given with their sizes, and we want to assign them to unit capacity bins such, that we use the minimum number of bins.In this paper, some generalizations of this problem are considered, where there are some additional stackability constraints defining that certain items can or cannot be packed on each other. The corresponding model in the literature is the Bin Packing Problem with Conflicts (BPPC), where this additional constraint is defined by an undirected conflict graph having edges between items that cannot be assigned to the same bin. However, we show some practical cases, where this conflict is directed, meaning that the items can be assigned to the same bin, but only in a certain order. Two new models are introduced for this problem: Bin Packing Problem with Hanoi Conflicts (BPPHC) and Bin Packing Problem with Directed Conflicts (BPPDC). In this work, the connection of the three conflict models is examined in detail.We have investigated the complexity of the new models, mainly the BPPHC model, in the special case where each item have the same size. We also considered two cases depending on whether re-ordering the items is allowed or not.We show that for the online version of the BPPHC model with unit size items, every Any-Fit algorithm gives not better than 3 when it is forbidden for the optimum to re-order the items, even if only 2 stackability classes, called Hanoi classes, are applied. This lower bound is generalized for arbitrary number of Hanoi classes. However, we also prove, that asymptotically the First-Fit algorithm is 1-competitive for this case.Finally, we introduce an algorithm for the offline version of the BP-PHC model with unit size items, which has polynomial time complexity, if the number of the Hanoi classes and the capacity of the bins are constant.

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Section: A Bódismentioning

confidence: 83%

Section: A Bódismentioning

confidence: 98%

Bin packing with directed stackability conflicts

Bódis

2015

Acta Universitatis Sapientiae, Informatica

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“…It is known that its value for classic online bin packing is 5 3 (Zhang 2002;). There are several other packing problems where an offline solution still needs to process the input as a sequence (Finlay and Manyem 2005;Epstein 2009;Dosa et al 2013;Chrobak et al 2011;Balogh et al 2015a, b;Böhm et al 2018).…”

Section: Introductionmentioning

confidence: 99%

More on ordered open end bin packing

Balogh

Epstein

Levin

2021

J Sched

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We consider the Ordered Open End Bin Packing problem. Items of sizes in (0, 1] are presented one by one, to be assigned to bins in this order. An item can be assigned to any bin for which the current total size is strictly below 1. This means also that the bin can be overloaded by its last packed item. We improve lower and upper bounds on the asymptotic competitive ratio in the online case. Specifically, we design the first algorithm whose asymptotic competitive ratio is strictly below 2, and its value is close to the lower bound. This is in contrast to the best possible absolute competitive ratio, which is equal to 2. We also study the offline problem where the sequence of items is known in advance, while items are still assigned to bins based on their order in the sequence. For this scenario, we design an asymptotic polynomial time approximation scheme.

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“…There are algorithms with smaller asymptotic competitive ratios, and the best possible asymptotic competitive ratio is known to be in [1.5403, 1.58889] [15,13,2]. Other variants of bin packing where the sequence of items must remain ordered even for offline solutions include Packing with LIB (largest item in the bottom) constraints, where an item can be packed into a bin with sufficient space if it is no larger than any item packed into this bin [11,6,12,5,4].…”

Section: Introductionmentioning

confidence: 99%

Colorful Bin Packing

Dósa

Epstein

2014

Algorithm Theory – SWAT 2014

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We study a variant of online bin packing, called colorful bin packing. In this problem, items that are presented one by one are to be packed into bins of size 1. Each item i has a size s i ∈ [0, 1] and a color c i ∈ C, where C is a set of colors (that is not necessarily known in advance). The total size of items packed into a bin cannot exceed its size, thus an item i can always be packed into a new bin, but an item cannot be packed into a non-empty bin if the previous item packed into that bin has the same color, or if the occupied space in it is larger than 1 − s i . This problem generalizes standard online bin packing and online black and white bin packing (where |C| = 2). We prove that colorful bin packing is harder than black and white bin packing in the sense that an online algorithm for zero size items that packs the input into the smallest possible number of bins cannot exist for |C| ≥ 3, while it is known that such an algorithm exists for |C| = 2. We show that natural generalizations of classic algorithms for bin packing fail to work for the case |C| ≥ 3, and moreover, algorithms that perform well for black and white bin packing do not perform well either, already for the case |C| = 3. Our main results are a new algorithm for colorful bin packing that we design and analyze, whose absolute competitive ratio is 4, and a new lower bound of 2 on the asymptotic competitive ratio of any algorithm, that is valid even for black and white bin packing.

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On online bin packing with LIB constraints

Cited by 13 publications

References 9 publications

Bin packing with directed stackability conflicts

Bin packing with directed stackability conflicts

More on ordered open end bin packing

Colorful Bin Packing

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