Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Approximation algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Bin Packing with Item Fragmentation
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Approximation Schemes for Scheduling on Uniformly Related and Identical Parallel Machines
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Lecture notes on approximation algorithms: Volume I
Lecture notes on approximation algorithms: Volume I
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Approximation schemes for packing with item fragmentation
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Matrix columns allocation problems
Theoretical Computer Science
On Lazy Bin Covering and Packing problems
Theoretical Computer Science
Approximation schemes for packing splittable items with cardinality constraints
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Approximation schemes for packing with item fragmentation
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
On lazy bin covering and packing problems
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Improved results for a memory allocation problem
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Mathematical programming algorithms for bin packing problems with item fragmentation
Computers and Operations Research
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We consider two variants of the classical bin packing problem in which items may be fragmented. This can potentially reduce the total number of bins needed for packing the instance. However, since fragmentation incurs overhead, we attempt to avoid it as much as possible. In bin packing with size increasing fragmentation (BP-SIF), fragmenting an item increases the input size (due to a header/footer of fixed size that is added to each fragment). In bin packing with size preserving fragmentation (BP-SPF), there is a bound on the total number of fragmented items. These two variants of bin packing capture many practical scenarios, including message transmission in community TV networks, VLSI circuit design and preemptive scheduling on parallel machines with setup times/setup costs. While both BP-SPF and BP-SIF do not belong to the class of problems that admit a polynomial time approximation scheme (PTAS), we show in this paper that both problems admit a dual PTAS and an asymptotic PTAS. We also develop for each of the problems a dual asymptotic fully polynomial time approximation scheme (AFPTAS). The AFPTASs are based on a non-trivial application of a fast combinatorial FPTAS for packing linear programs with negative entries, proposed recently by Garg and Khandekar [5].