1-Bounded Space Algorithms for 2-Dimensional Bin Packing
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Two-dimensional online bin packing with rotation
Theoretical Computer Science
A novel strategy for multi-resource load balancing in agent-based systems
International Journal of Intelligent Information and Database Systems
Dynamic multi-dimensional bin packing
Journal of Discrete Algorithms
A new upper bound 2.5545 on 2D Online Bin Packing
ACM Transactions on Algorithms (TALG)
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
Improved online hypercube packing
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Bounds for online bounded space hypercube packing
Discrete Optimization
Online algorithms for 1-space bounded multi dimensional bin packing and hypercube packing
Journal of Combinatorial Optimization
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We solve an open problem in the literature by providing an online algorithm for multidimensional bin packing that uses only bounded space. To achieve this, we introduce a new technique for classifying the items to be packed. We show that our algorithm is optimal among bounded space algorithms for any dimension $d1$. Its asymptotic performance ratio is $(\Pi_{\infty})^d$, where $\Pi_{\infty}\approx1.691$ is the asymptotic performance ratio of the one-dimensional algorithm \harm. A modified version of this algorithm for the case where all items are hypercubes is also shown to be optimal. Its asymptotic performance ratio is sublinear in $d$.Furthermore, we extend the techniques used in these algorithms to give optimal algorithms for online bounded space variable-sized packing and resource augmented packing.