A simple on-line bin-packing algorithm
Journal of the ACM (JACM)
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
Improved space for bounded-space, on-line bin-packing
SIAM Journal on Discrete Mathematics
On the asymptotic worst case behavior of harmonic fit
Journal of Algorithms
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
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
On-line Packing and Covering Problems
Developments from a June 1996 seminar on Online algorithms: the state of the art
Theoretical Computer Science - Latin American theoretical informatics
Worst-case analysis of memory allocation algorithms
STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
Approximation schemes for multidimensional packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
New approximability and inapproximability results for 2-dimensional Bin Packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
New approximability and inapproximability results for 2-dimensional Bin Packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Three dozen papers on online algorithms
ACM SIGACT News
EDAS: providing an environment for decentralized adaptive services
DSM '05 Proceedings of the 2nd international doctoral symposium on Middleware
ACM Transactions on Algorithms (TALG)
Bin Packing in Multiple Dimensions: Inapproximability Results and Approximation Schemes
Mathematics of Operations Research
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
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 bin packing with cardinality constraints
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Online removable square packing
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Improved online hypercube packing
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Multi-dimensional packing with conflicts
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
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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 d 1. Its asymptotic performance ratio is (II∞)d, where II∞ ≈ 1:691 is the asymptotic performance ratio of the one-dimensional algorithm HARMONIC. 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.Additionally, for the special case of packing squares in two-dimensional bins, we present a new unbounded space online algorithm with asymptotic performance ratio of at most 2.271. We also present an approximation algorithm for the offline problem with approximation ratio of 16/11.