Online LIB problems: Heuristics for Bin Covering and lower bounds for Bin Packing

Finlay, Luke; Manyem, Prabhu

doi:10.1051/ro:2006001

Cited by 8 publications

(5 citation statements)

References 8 publications

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“…In the online bin packing problem with LIB (Larger Item in the Bottom) constraints [4,[9][10][11], the subsequence of items which are packed into one bin, a j 1 , a j 2 , . .…”

Section: Alg(i ) Opt(i )mentioning

confidence: 99%

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On online bin packing with LIB constraints

Epstein

2009

Naval Research Logistics

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In many applications of packing, the location of small items below large items, inside the packed boxes, is forbidden. We consider a variant of the classic online one-dimensional bin packing, in which items allocated to each bin are packed there in the order of arrival, satisfying the condition above. This variant is called online bin packing problem with LIB (larger item in the bottom) constraints. We give an improved analysis of First Fit showing that its competitive ratio is at most 5 2 = 2.5, and design a lower bound of 2 on the competitive ratio of any online algorithm. In addition, we study the competitive ratio of First Fit as a function of an upper bound(where d is a positive integer) on the item sizes. Our upper bound on the competitive ratio of First Fit tends to 2 as d grows, whereas the lower bound of two holds for any value of d. Finally, we consider several natural and well known algorithms, namely, Best Fit, Worst Fit, Almost Worst Fit, and Harmonic, and show that none of them has a finite competitive ratio for the problem.

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“…In the online bin packing problem with LIB (Larger Item in the Bottom) constraints [4,[9][10][11], the subsequence of items which are packed into one bin, a j 1 , a j 2 , . .…”

Section: Alg(i ) Opt(i )mentioning

confidence: 99%

“…They showed that the competitive ratio of this class of algorithms is at least 2. As for lower bounds, a lower bound of 1.78 on the competitive ratio of any algorithm was claimed in [4]. Unfortunately, there seems to be an error in this proof.…”

Section: Previous Workmentioning

confidence: 99%

On online bin packing with LIB constraints

Epstein

2009

Naval Research Logistics

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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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“…It is known that its value for classic online bin packing is 5 3 [30,6]. There are several other packing problems where an offline solution still needs to process the input as a sequence [17,13,12,11,1,2,10].…”

Section: Introductionmentioning

confidence: 99%

More on ordered open end bin packing

Balogh¹,

Epstein²,

Levin³

2020

Preprint

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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 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 it is close to the lower bound. This is in contrast to the best possible absolute approximation 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.

show abstract

Online LIB problems: Heuristics for Bin Covering and lower bounds for Bin Packing

Cited by 8 publications

References 8 publications

On online bin packing with LIB constraints

On online bin packing with LIB constraints

More on ordered open end bin packing

More on ordered open end bin packing

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