Online algorithms for a dual version of bin packing
Discrete Applied Mathematics
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Better approximation algorithms for bin covering
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
An asymptotic fully polynomial time approximation scheme for bin covering
Theoretical Computer Science
The Ordered Open-End Bin-Packing Problem
Operations Research
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
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
Set covering with ordered replacement: additive and multiplicative gaps
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Hardness of lazy packing and covering
Operations Research Letters
The lazy bureaucrat problem with common arrivals and deadlines: approximation and mechanism design
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
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We consider three variants of the open-end bin packing problem. Such variants of bin packing allow the total size of items packed into a bin to exceed the capacity of a bin, provided that a removal of the last item assigned to a bin would bring the contents of the bin below the capacity. In the first variant, this last item is the minimum sized item in the bin, that is, each bin must satisfy the property that the removal of any item should bring the total size of items in the bin below 1. The next variant (which is also known as lazy bin covering is similar to the first one, but in addition to the first condition, all bins (expect for possibly one bin) must contain a total size of items of at least 1. We show that these two problems admit asymptotic fully polynomial time approximation schemes (AFPTAS). Moreover, they turn out to be equivalent. We briefly discuss a third variant, where the input items are totally ordered, and the removal of the maximum indexed item should bring the total size of items in the bin below 1, and show that this variant is strongly NP-hard.