A simple on-line bin-packing algorithm
Journal of the ACM (JACM)
Improved bounds for harmonic-based bin packing algorithms
Discrete Applied Mathematics - Special volume: combinatorics and theoretical computer science
An improved lower bound for on-line bin packing algorithms
Information Processing Letters
New bounds for multi-dimensional packing
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Two-Dimensional On-Line Bin Packing Problem with Rotatable Items
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
1-Bounded Space Algorithms for 2-Dimensional Bin Packing
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
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In this paper, we study the problem of packing rectangular items into a minimum number of square grids in an on-line manner with a single active grid, where the size of each grid is m 脳 m for some positive integer m, and the height and the width of each item are positive integers smaller than or equal to m, respectively. We first prove that the asymptotic competitive ratio of an optimal on-line algorithm is at least 23/11. We then propose an on-line algorithm that achieves a competitive ratio O((log logm)2)