Online algorithms for a dual version of bin packing
Discrete Applied Mathematics
Optimal bin covering with items of random size
SIAM Journal on Computing
A note for optimal bin packing and optimal bin covering with items of random size
SIAM Journal on Computing
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Probabilistic analysis of algorithms for dual bin packing problems
Journal of Algorithms
Probability
Biased random walks, Lyapunov functions, and stochastic analysis of best fit bin packing
Journal of Algorithms
Two simple algorithms for bin covering
Acta Cybernetica
Average-case analyses of first fit and random fit bin packing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
On the sum-of-squares algorithm for bin packing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
SIAM Journal on Discrete Mathematics
Probabilistic analysis of a bin covering algorithm
Operations Research Letters
An Asymptotic Fully Polynomial Time Approximation Scheme for Bin Covering
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
An asymptotic fully polynomial time approximation scheme for bin covering
Theoretical Computer Science
On the Sum-of-Squares algorithm for bin packing
Journal of the ACM (JACM)
Bin packing problems with rejection penalties and their dual problems
Information and Computation
The maximum resource bin packing problem
Theoretical Computer Science
Distributed Approximation Algorithm for Resource Clustering
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Asymptotic fully polynomial approximation schemes for variants of open-end bin packing
Information Processing Letters
A Distributed Algorithm for Resource Clustering in Large Scale Platforms
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
Hardness of approximation for orthogonal rectangle packing and covering problems
Journal of Discrete Algorithms
Bin completion algorithms for multicontainer packing, knapsack, and covering problems
Journal of Artificial Intelligence Research
Bounded-space online bin cover
Journal of Scheduling
Bin packing problems with rejection penalties and their dual problems
Information and Computation
On the sum minimization version of the online bin covering problem
Discrete Applied Mathematics
Approximation algorithms for min-max generalization problems
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
The train delivery problem: vehicle routing meets bin packing
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Theoretical Computer Science
Bin packing and covering problems with rejection
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
On lazy bin covering and packing problems
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
The maximum resource bin packing problem
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Improved approximation algorithms for maximum resource bin packing and lazy bin covering problems
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Hardness of lazy packing and covering
Operations Research Letters
Bin covering with cardinality constraints
Discrete Applied Mathematics
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Bin covering takes as input a list of items with sizes in (0, 1) and places them into bins of unit demand so as to maximize the number of bins whose demand is satisfied. This is in a sense a dual problem to the classical one-dimensional bin packing problem, but has for many years lagged behind the latter in terms of the quality of the best approximation algorithms. We design algorithms for this problem that close the gap, both in terms of worst- and average-case results. We present (1) the first asymptotic approximation scheme for the offline version, (2) algorithms that have bounded worst-case behavior for instances with discrete item sizes and expected behavior that is asymptotically optimal for all discrete “perfect-packing distributions” (ones for which optimal packings have sublinear expected waste), and (3) a learning algorithm that has asymptotically optimal expected behavior for all discrete distributions. The algorithms of (2) and (3) are based on the recently-developed online Sum-of-Squares algorithm for bin packing. We also present experimental analysis comparing the algorithms of (2) and suggesting that one of them, the Sum-of-Squares-with-Threshold algorithm, performs quite well even for discrete distributions that do not have the perfect-packing property.