Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
SIAM Journal on Computing
An efficient approximation scheme for variable-sized bin packing
SIAM Journal on Computing
Fast approximation algorithms for fractional packing and covering problems
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Using fast matrix multiplication to find basic solutions
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximate Max-Min Resource Sharing for Structured Concave Optimization
SIAM Journal on Optimization
On Preemptive Resource Constrained Scheduling: Polynomial-Time Approximation Schemes
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
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
Sequential and Parallel Algorithms for Mixed Packing and Covering
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Lecture notes on approximation algorithms: Volume I
Lecture notes on approximation algorithms: Volume I
Approximation Schemes for Packing with Item Fragmentation
Theory of Computing Systems
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Preemptive scheduling of independent jobs on identical parallel machines subject to migration delays
ESA'05 Proceedings of the 13th annual European conference on Algorithms
A robust APTAS for the classical bin packing problem
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
AFPTAS Results for Common Variants of Bin Packing: A New Method for Handling the Small Items
SIAM Journal on Optimization
An improved approximation scheme for variable-sized bin packing
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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Motivated from recent applications in community TV networks and VLSI circuit design, we study variants of the classic bin packing problem, in which a set of items needs to be packed in a minimum number of unit-sized bins, allowing items to be fragmented. This can potentially reduce the total number of bins used, however, item fragmentation does not come for free. In bin packing with size preserving fragmentation (BP-SPF), there is a bound on the total number of fragmented items. 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). Both BP-SPF and BP-SIF do not belong to the class of problems that admit a polynomial time approximation scheme (PTAS). In this paper, we develop fast asymptotic fully polynomial time approximation schemes (AFPTAS) for both problems. The running times of our schemes are linear in the input size. As special cases, our schemes yield AFPTASs for classical bin packing and for variable-sized bin packing, whose running times improve the best known running times for these problems.