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
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)
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
On the online bin packing problem
Journal of the ACM (JACM)
On-line grid-packing with a single active grid
Information Processing Letters
Packing 2-Dimensional Bins in Harmony
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
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
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
A new upper bound 2.5545 on 2D Online Bin Packing
ACM Transactions on Algorithms (TALG)
Bounds for online bounded space hypercube packing
Discrete Optimization
Multidimensional on-line bin packing: Algorithms and worst-case analysis
Operations Research Letters
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In this paper, we study 1-space bounded multi-dimensional bin packing and hypercube packing. A sequence of items arrive over time, each item is a d-dimensional hyperbox (in bin packing) or hypercube (in hypercube packing), and the length of each side is no more than 1. These items must be packed without overlapping into d-dimensional hypercubes with unit length on each side. In d-dimensional space, any two dimensions i and j define a space P ij . When an item arrives, we must pack it into an active bin immediately without any knowledge of the future items, and 90驴-rotation on any plane P ij is allowed.The objective is to minimize the total number of bins used for packing all these 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. For d-dimensional bin packing, an online algorithm with competitive ratio 4 d is given. Moreover, we consider d-dimensional hypercube packing, and give a 2 d+1-competitive algorithm. These two results are the first study on 1-space bounded multi dimensional bin packing and hypercube packing.