Computer algorithms: introduction to design and analysis
Computer algorithms: introduction to design and analysis
Online algorithms for a dual version of bin packing
Discrete Applied Mathematics
Improved bounds for harmonic-based bin packing algorithms
Discrete Applied Mathematics - Special volume: combinatorics and theoretical computer science
An improved lower bound for on-line bin packing algorithms
Information Processing Letters
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Multiprocessor Scheduling with Rejection
SIAM Journal on Discrete Mathematics
Better approximation algorithms for bin covering
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Preemptive multiprocessor scheduling with rejection
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
On the online bin packing problem
Journal of the ACM (JACM)
On-line Packing and Covering Problems
Developments from a June 1996 seminar on Online algorithms: the state of the art
An asymptotic fully polynomial time approximation scheme for bin covering
Theoretical Computer Science
Bin packing and covering problems with rejection
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
On-line scheduling of unit time jobs with rejection: minimizing the total completion time
Operations Research Letters
A fast asymptotic approximation scheme for bin packing with rejection
Theoretical Computer Science
Bin packing with controllable item sizes
Information and Computation
Online unit clustering: Variations on a theme
Theoretical Computer Science
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In this paper we consider the following problems: we are given a set of n items {u1,....,un} and a number of unit-capacity bins. Each item ui has a size wi ∈ (0, 1] and a penalty pi ≥ 0. An item can be either rejected, in which case we pay its penalty, or put into one bin under the constraint that the total size of the items in the bin is no greater than 1. No item can be spread into more than one bin. The objective is to minimize the total number of used bins plus the total penalty paid for the rejected items. We call the problem bin packing with rejection penalties, and denote it as BPR. For the on-line BPR problem, we present an algorithm with an absolute competitive ratio of 2.618 while the lower bound is 2.343, and an algorithm with an asymptotic competitive ratio arbitrarily close to 1.75 while the lower bound is 1.540. For the off-line BPR problem, we present an algorithm with an absolute worst-case ratio of 2 while the lower bound is 1.5, and an algorithm with an asymptotic worst-case ratio of 1.5. We also study a closely related bin covering version of the problem. In this case pi means some amount of profit. If an item is rejected, we get its profit, or it can be put into a bin in such a way that the total size of the items in the bin is no smaller than 1. The objective is to maximize the number of covered bins plus the total profit of all rejected items. We call this problem bin covering with rejection (BCR). For the on-line BCR problem, we show that no algorithm can have absolute competitive ratio greater than 0, and present an algorithm with asymptotic competitive ratio 1/2, which is the best possible. For the off-line BCR problem, we also present an algorithm with an absolute worst-case ratio of 1/2 which matches the lower bound.