SIAM Journal on Computing
An efficient approximation scheme for variable-sized bin packing
SIAM Journal on Computing
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Multiprocessor Scheduling with Rejection
SIAM Journal on Discrete Mathematics
Approximation algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
SIAM Journal on Computing
Bin packing problems with rejection penalties and their dual problems
Information and Computation
Bin packing with rejection revisited
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Bin packing with controllable item sizes
Information and Computation
AFPTAS Results for Common Variants of Bin Packing: A New Method for Handling the Small Items
SIAM Journal on Optimization
The entropy rounding method in approximation algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Hi-index | 5.23 |
''Bin packing with rejection'' is the following problem: Given a list of items with associated sizes and rejection costs, find a packing into unit bins of a subset of the list such that the number of bins used plus the sum of rejection costs of unpacked items is minimized. We show that bin packing with rejection can be reduced to n multiple knapsack problems and, based on techniques for the multiple knapsack problem, we give a fast asymptotic polynomial time approximation scheme,''Reject&Pack'', with time complexity O(n^O^(^@e^^^-^^^2^)). This improves a recent approximation scheme given by Epstein, which has time complexity O(n^O^(^(^@e^^^-^^^4^)^^^@e^^^^^^^-^^^^^^^1^)). We also show that Reject&Pack can be extended to variable-sized bin packing with rejection and give an asymptotic polynomial time approximation scheme.