A fundamental restriction on fully dynamic maintenance of bin packing

doi:10.1016/0020-0190(96)00112-3

Information Processing Letters

Volume 59, Issue 4, 26 August 1996, Pages 229-232

https://doi.org/10.1016/0020-0190(96)00112-3 Get rights and content

Abstract

This paper studies a fundamental restriction on the problem of maintaining an approximate solution for one-dimensional bin packing when items may arrive and depart dynamically. It is shown that imposing a fixed constant upper bound on the number of items that can be moved between bins per Insert/Delete operation forces the competitive ratio to be at least $43$ , regardless of the running time allowed per Insert/Delete. Thus, the ability to move more than a constant number of items is necessary for accomplishing highly competitive, time-efficient fully dynamic approximation algorithms for bin packing.

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There are more references available in the full text version of this article.

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Combining admission tests for heuristic partitioning of real-time tasks on ARM big.LITTLE multi-processor architectures
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Citation Excerpt :
Gambosi [10] allows a constant number of elements to move from one bin to another, as a consequence of the arrival of a new input element, and possible algorithms are presented. Ivković [11] shows that the ability to move more than a constant number of items is necessary for accomplishing highly competitive, time-efficient fully dynamic approximation algorithms for bin packing. Balogh [12] continues the work in [11] by improving the lower bound on the asymptotic worst-case ratio, while [13] uses a new dynamic rounding technique and novel methods to handle small items in a dynamic setting such that no amortization is needed.
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We study on-line bounded space bin-packing in the resource augmentation model of competitive analysis. In this model, the on-line bounded space packing algorithm has to pack a list $L$ of items with sizes in (0, 1], into a minimum number of bins of size $b$ , $b \geq 1$ . A bounded space algorithm has the property that it only has a constant number of active bins available to accept items at any point during processing. The performance of the algorithm is measured by comparing the produced packing with an optimal offline packing of the list $L$ into bins of size 1. The competitive ratio then becomes a function of the on-line bin size $b$ . Csirik and Woeginger studied this problem in [J. Csirik, G.J. Woeginger, Resource augmentation for online bounded space bin packing, Journal of Algorithms 44(2) (2002) 308–320] and proved that no on-line bounded space algorithm can perform better than a certain bound $ρ (b)$ in the worst case. We relax the on-line condition by allowing a complete repacking within the active bins, and show that the same lower bound holds for this problem as well, and repacking may only allow one to obtain the exact best possible competitive ratio of $ρ (b)$ having a constant number of active bins, instead of achieving this bound in the limit. We design a polynomial time on-line algorithm that uses three active bins and achieves the exact best possible competitive ratio $ρ (b)$ for the given problem.
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Fully-dynamic bin packing with limited repacking
2017, arXiv
A tight approximation for fully dynamic bin packing without bundling
2017, arXiv

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^☆: Partially supported by the National Science Foundation under Grant CCR-9120731.

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A fundamental restriction on fully dynamic maintenance of bin packing☆

Abstract

Parallel approximation algorithms for bin packing

Inform. and Comput.

A lower bound for on-line one-dimensional bin packing algorithms

Dynamic bin packing

SIAM J. Comput.

Approximation algorithms for bin packing: An updated survey

Introduction to Algorithms

Bin packing can be solved within 1 + ε in linear time

Combinatorica