A simple on-line bin-packing algorithm
Journal of the ACM (JACM)
On-line bin packing in linear time
Journal of Algorithms
Journal of Parallel and Distributed Computing
An improved lower bound for on-line bin packing algorithms
Information Processing Letters
New Algorithms for Bin Packing
Journal of the ACM (JACM)
On the online bin packing problem
Journal of the ACM (JACM)
Packing 2-Dimensional Bins in Harmony
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On-Line Grid-Packing with a Single Active Grid
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Optimal Online Algorithms for Multidimensional Packing Problems
SIAM Journal on Computing
Improved approximation algorithms for multidimensional bin packing problems
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Bin Packing in Multiple Dimensions: Inapproximability Results and Approximation Schemes
Mathematics of Operations Research
Online Removable Square Packing
Theory of Computing Systems
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In this paper, we study the bounded space variation, especially 1-bounded space, of 2-dimensional bin packing. A sequence of rectangular items arrive over time, and the following item arrives after the packing of the previous one. The height and width of each item are no more than 1, we need to pack these items into unit square bins of size 1脳1 and our objective is to minimize the number of used bins. Once an item is packed into a square bin, the position of this item is fixed and it cannot be shifted within this bin. At any time, there is at most one active bin; the current unpacked item can be only packed into the active bin and the inactive bins (closed at some previous time) cannot be used for any future items. We first propose an online algorithm with a constant competitive ratio 12, then improve the competitive ratio to 8.84 by the some complicated analysis. Our results significantly improve the previous best known O((loglogm)2)-competitive algorithm[10], where m is the width of the square bin and the size of each item is a脳b, where a, b are integers no more than m. Furthermore, the lower bound for the competitive ratio is also improved to 2.5.