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
Mathematics of Operations Research
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
An asymptotic fully polynomial time approximation scheme for bin covering
Theoretical Computer Science
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
Class constrained bin packing revisited
Theoretical Computer Science
Approximation algorithms for min-max and max-min resource sharing problems, and applications
Efficient Approximation and Online Algorithms
Fast asymptotic FPTAS for packing fragmentable items with costs
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
The tight bound of first fit decreasing bin-packing algorithm is FFD(I) ≤ 11/9OPT(I) + 6/9
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
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The variable-sized bin packing problem (VBP) is a well-known generalization of the NP-hard bin packing problem (BP) where the items can be packed in bins of M given sizes. The objective is to minimize the total capacity of the bins used. We present an AFPTAS for VBP and BP with performance guarantee $P(I) \leq (1+ \varepsilon )OPT(I) + O(\log^2(\frac{1}{\varepsilon }))$. The additive term is much smaller than the additive term of already known AFPTAS. The running time of the algorithm is $O( \frac{1}{\varepsilon ^6} \log\left(\frac{1}{\varepsilon }\right) + \log\left(\frac{1}{\varepsilon }\right) n)$ for bin packing and $O(\frac{1}{\varepsilon ^{7}} \log^2\left(\frac{1}{\varepsilon }\right) + \log\left(\frac{1}{\varepsilon }\right)\left(M+n\right))$ for variable-sized bin packing, which is an improvement to previously known algorithms.