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
Online algorithm for 1-space bounded multi-dimensional bin packing
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
On-line algorithms for 2-space bounded 2-dimensional bin packing
Information Processing Letters
Online algorithms for 1-space bounded multi dimensional bin packing and hypercube packing
Journal of Combinatorial Optimization
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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 × 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 prove two elementary bounds on the asymptotic competitive ratio of an optimal on-line algorithm, that is at least 23/11 and at most (4/13)√m- o(√m). We then propose an on-line algorithm that achieves a competitive ratio O((log log m)2).