A simple on-line bin-packing algorithm
Journal of the ACM (JACM)
Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
SIAM Journal on Computing
Online algorithms for a dual version of bin packing
Discrete Applied Mathematics
On-line bin packing in linear time
Journal of Algorithms
An on-line algorithm for variable-sized bin packing
Acta Informatica
An improved lower bound for on-line bin packing algorithms
Information Processing Letters
Improved space for bounded-space, on-line bin-packing
SIAM Journal on Discrete Mathematics
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
There is no asymptotic PTAS for two-dimensional vector packing
Information Processing Letters
Approximation Algorithms for the Discrete Time-Cost Tradeoff Problem
Mathematics of Operations Research
On the online bin packing problem
Journal of the ACM (JACM)
An Optimal Online Algorithm for Bounded Space Variable-Sized Bin Packing
SIAM Journal on Discrete Mathematics
New Bounds for Variable-Sized Online Bin Packing
SIAM Journal on Computing
On-line Packing and Covering Problems
Developments from a June 1996 seminar on Online algorithms: the state of the art
Bin packing problems with rejection penalties and their dual problems
Information and Computation
Bin Packing in Multiple Dimensions: Inapproximability Results and Approximation Schemes
Mathematics of Operations Research
A fast asymptotic approximation scheme for bin packing with rejection
Theoretical Computer Science
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Fast algorithms for bin packing
Journal of Computer and System Sciences
Inapproximability results for orthogonal rectangle packing problems with rotations
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Optimal on-line algorithms for variable-sized bin covering
Operations Research Letters
Vector bin packing with multiple-choice
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Vector bin packing with multiple-choice
Discrete Applied Mathematics
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We consider a natural resource allocation problem in which we are given a set of items, where each item has a list of pairs associated with it. Each pair is a configuration of an allowed size for this item, together with a nonnegative penalty, and an item can be packed using any configuration in its list. The goal is to select a configuration for each item so that the number of unit bins needed to pack the sizes plus the sum of penalties is minimized. This problem has applications in operating systems, bandwidth allocation, and discrete time-cost tradeoff planning problems. For the offline version of the problem we design an augmented asymptotic PTAS. That is, an asymptotic approximation scheme that uses bins of size slightly larger than 1. We further consider the online bounded space variant, where only a constant number of bins can be open simultaneously. We design a sequence of algorithms, where the sequence of their competitive ratios tends to the best possible asymptotic competitive ratio. Finally, we study the bin covering problem, in which a bin is covered if the sum of sizes allocated to it is at least 1. In this setting, penalties are interpreted as profits and the goal is to maximize the sum of profits plus the number of covered bins. We design an algorithm of best possible competitive ratio, which is 2. We generalize our results for online algorithms and unit sized bins to the case of variable sized bins, where there may be several distinct sizes of bins available for packing or covering, and get that the competitive ratios are again the same as for the more standard online problems.