A simple on-line bin-packing algorithm
Journal of the ACM (JACM)
On-line bin packing in linear time
Journal of Algorithms
An improved lower bound for on-line bin packing algorithms
Information Processing Letters
Two-dimensional rectangle packing: on-line methods and results
Discrete Applied Mathematics - ARIDAM IV and V
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
Theoretical Computer Science - Latin American theoretical informatics
Optimal online bounded space multidimensional packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal Online Algorithms for Multidimensional Packing Problems
SIAM Journal on Computing
Bin Packing in Multiple Dimensions: Inapproximability Results and Approximation Schemes
Mathematics of Operations Research
SIAM Journal on Computing
Improved online hypercube packing
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Two-dimensional online bin packing with rotation
Theoretical Computer Science
SIGACT news online algorithms column 20: the power of harmony
ACM SIGACT News
Online algorithms for 1-space bounded multi dimensional bin packing and hypercube packing
Journal of Combinatorial Optimization
Hi-index | 0.00 |
The 2D Online Bin Packing is a fundamental problem in Computer Science and the determination of its asymptotic competitive ratio has research attention. In a long series of papers, the lower bound of this ratio has been improved from 1.808, 1.856 to 1.907 and its upper bound reduced from 3.25, 3.0625, 2.8596, 2.7834 to 2.66013. In this article, we rewrite the upper bound record to 2.5545. Our idea for the improvement is as follows. In 2002, Seiden and van Stee [Seiden and van Stee 2003] proposed an elegant algorithm called H ⊗ C, comprised of the Harmonic algorithm H and the Improved Harmonic algorithm C, for the two-dimensional online bin packing problem and proved that the algorithm has an asymptotic competitive ratio of at most 2.66013. Since the best known online algorithm for one-dimensional bin packing is the Super Harmonic algorithm [Seiden 2002], a natural question to ask is: could a better upper bound be achieved by using the Super Harmonic algorithm instead of the Improved Harmonic algorithm? However, as mentioned in Seiden and van Stee [2003], the previous analysis framework does not work. In this article, we give a positive answer for this question. A new upper bound of 2.5545 is obtained for 2-dimensional online bin packing. The main idea is to develop new weighting functions for the Super Harmonic algorithm and propose new techniques to bound the total weight in a rectangular bin.