Amortized efficiency of list update and paging rules
Communications of the ACM
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Online computation and competitive analysis
Online computation and competitive analysis
An approximation algorithm for the maximum traveling salesman problem
Information Processing Letters
Two simple algorithms for bin covering
Acta Cybernetica
Better approximation algorithms for bin covering
SODA '01 Proceedings of the twelfth 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
The Lazy Bureaucrat scheduling problem
Information and Computation
An asymptotic fully polynomial time approximation scheme for bin covering
Theoretical Computer Science
Windows scheduling as a restricted version of Bin Packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The relative worst order ratio for on-line algorithms
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
Online interval coloring and variants
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
ACM SIGACT News
On lazy bin covering and packing problems
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
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
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Usually, for bin packing problems, we try to minimize the number of bins used or in the case of the dual bin packing problem, maximize the number or total size of accepted items. This paper presents results for the opposite problems, where we would like to maximize the number of bins used or minimize the number or total size of accepted items. We consider off-line and on-line variants of the problems. For the off-line variant, we require that there be an ordering of the bins, so that no item in a later bin fits in an earlier bin. We find the approximation ratios of two natural approximation algorithms, First-Fit-Increasing and First-Fit-Decreasing for the maximum resource variant of classical bin packing. For the on-line variant, we define maximum resource variants of classical and dual bin packing. For dual bin packing, no on-line algorithm is competitive. For classical bin packing, we find the competitive ratio of various natural algorithms. We study the general versions of the problems as well as the parameterized versions where there is an upper bound of $\frac{1}{k}$ on the item sizes, for some integer k.