An improved lower bound for on-line bin packing algorithms

C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c aOnline Bin Packing with Resource Augmentation ABSTRACT In competitive analysis, we usually do not put any restrictions on the computational complexity of online algorithms, although efficient algorithms are preferred. Thus if such an algorithm were given the entire input in advance, it could give an optimal solution (in exponential time). Instead of giving the algorithm more knowledge about the input, in this paper we consider the effects of giving an online bin packing algorithm larger bins than the offline algorithm it is compared to. We give new algorithms for this problem that combine items in bins in an unusual way and give bounds on their performance which improve upon the best possible bounded space algorithm. We also give general lower bounds for this problem which are nearly matching for bin sizes b 2. AbstractIn competitive analysis, we usually do not put any restrictions on the computational complexity of online algorithms, although efficient algorithms are preferred. Thus if such an algorithm were given the entire input in advance, it could give an optimal solution (in exponential time). Instead of giving the algorithm more knowledge about the input, in this paper we consider the effects of giving an online bin packing algorithm larger bins than the offline algorithm it is compared to. We give new algorithms for this problem that combine items in bins in an unusual way and give bounds on their performance which improve upon the best possible bounded space algorithm. We also give general lower bounds for this problem which are nearly matching for bin sizes b ≥ 2.

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“…Yao showed that REVISED FIRST FIT has performance ratio 5 3 . Currently the best known lower bound is 1.54014, due to van Vliet [15].…”

Section: Previous Resultsmentioning

confidence: 99%

Online Bin Packing with Resource Augmentation

Epstein

Stee

2005

Approximation and Online Algorithms

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“…As for the lower bound of the competitive ratio, Yao [24] showed that no online algorithm can have an asymptotic competitive ratio less than 1.5. The best known lower bound to date is 1.54014 [23].…”

Section: Related Workmentioning

confidence: 99%

Improved Online Algorithms for 1-Space Bounded 2-Dimensional Bin Packing

Zhang

Chen

Chin

et al. 2010

Algorithms and Computation

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Abstract. In this paper, we study 1-space bounded 2-dimensional bin packing and square packing. A sequence of rectangular items (square items, respectively) arrive over time, which must be packed into square bins of size 1×1. 90 • -rotation of an item is allowed. When an item arrives, we must pack it into an active bin immediately without any knowledge of the future items. The objective is to minimize the total number of bins used for packing all the items in the sequence. In the 1-space bounded variant, there is only one active bin for packing the current item. If the active bin does not have enough space to pack the item, it must be closed and a new active bin is opened. Our contributions are as follows: For 1-space bounded 2-dimensional bin packing, we propose an online packing strategy with competitive ratio 5.155, surpassing the previous 8.84-competitive bound. The lower bound of competitive ratio is also improved from 2.5 to 3. Furthermore, we study 1-space bounded square packing, which is a special case of the bin packing problem. We give a 4.5-competitive packing algorithm, and prove that the lower bound of competitive ratio is at least 8/3.

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“…It is wellknown that the problem is NP-hard [11]. In the online setting [14,15], items may arrive at arbitrary time; item arrival time and item size are only known when an item arrives. The performance of an online algorithm is measured using competitive analysis [3].…”

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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An improved lower bound for on-line bin packing algorithms

Cited by 166 publications

References 4 publications

Online Bin Packing with Resource Augmentation

Online Bin Packing with Resource Augmentation

Improved Online Algorithms for 1-Space Bounded 2-Dimensional Bin Packing

An 8/3 Lower Bound for Online Dynamic Bin Packing

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