SIAM Journal on Computing
An efficient approximation scheme for variable-sized bin packing
SIAM Journal on Computing
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
Approximate Algorithms for the 0/1 Knapsack Problem
Journal of the ACM (JACM)
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
New Bounds for Variable-Sized Online Bin Packing
SIAM Journal on Computing
Heuristic Solutions for the Multiple-Choice Multi-dimension Knapsack Problem
ICCS '01 Proceedings of the International Conference on Computational Science-Part II
Quality adaptation in a multisession multimedia system: model, algorithms, and architecture
Quality adaptation in a multisession multimedia system: model, algorithms, and architecture
On Multidimensional Packing Problems
SIAM Journal on Computing
Solving the multidimensional multiple-choice knapsack problem by constructing convex hulls
Computers and Operations Research
Improved approximation algorithms for multidimensional bin packing problems
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of 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
Bin packing with controllable item sizes
Information and Computation
An APTAS for Generalized Cost Variable-Sized Bin Packing
SIAM Journal on Computing
A New Heuristic for Solving the Multichoice Multidimensional Knapsack Problem
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
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We consider a variant of bin packing called multiple-choice vector bin packing. In this problem, we are given a set of n items, where each item can be selected in one of several D-dimensional incarnations. We are also given T bin types, each with its own cost andD-dimensional size. Our goal is to pack the items in a set of bins of minimum overall cost. The problem is motivated by scheduling in networks with guaranteed quality of service (QoS), but due to its general formulation it has many other applications as well. We present an approximation algorithm that is guaranteed to produce a solution whose cost is about lnD times the optimum. For the running time to be polynomial we require D=O(1) and T=O(logn). This extends previous results for vector bin packing, in which each item has a single incarnation and there is only one bin type. To obtain our result we also present a PTAS for the multiple-choice version of multidimensional knapsack, where we are given only one bin and the goal is to pack a maximum weight set of (incarnations of) items in that bin.