Disk load balancing for video-on-demand systems
Multimedia Systems
Design and implementation of scalable continuous media servers
Parallel Computing - Special issues on applications: parallel data servers and applications
There is no asymptotic PTAS for two-dimensional vector packing
Information Processing Letters
Scheduling unrelated machines with costs
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
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)
`` Strong '' NP-Completeness Results: Motivation, Examples, and Implications
Journal of the ACM (JACM)
Continuous Media Sharing in Multimedia Database Systems
Proceedings of the 4th International Conference on Database Systems for Advanced Applications (DASFAA)
Threshold-Based Dynamic Replication in Large-Scale Video-on-Demand Systems
RIDE '98 Proceedings of the Workshop on Research Issues in Database Engineering
On Multidimensional Packing Problems
SIAM Journal on Computing
Tight approximation algorithms for maximum general assignment problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
SIAM Journal on Computing
Algorithms for non-uniform size data placement on parallel disks
Journal of Algorithms
Scheduling Techniques for Media-on-Demand
Algorithmica
Approximation algorithms for data placement on parallel disks
ACM Transactions on Algorithms (TALG)
Vector bin packing with multiple-choice
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
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Given is a set of items and a set of devices, each possessing two limited resources. Each item requires some amounts of these resources. Further, each item is associated with a profit and a color, and items of the same color can share the use of one resource. The goal is to allocate the resources to the most profitable (feasible) subset of items. In alternative formulation, the goal is to pack the most profitable subset of items in a set of two-dimensional bins (knapsacks), in which the capacity in one dimension is sharable. Indeed, the special case where there is a single item in each color is the well-known two-dimensional vector packing (2DVP) problem. Thus, unless P = NP, the problem that we study does not admit a fully polynomial time approximation scheme (FPTAS) for a single bin, and is MAX-SNP hard for multiple bins. Our problem has several important applications, including data placement on disks in media-on-demand systems. We present approximation algorithms as well as optimal solutions for some instances. In some cases, our results are similar to the best known results for 2DVP. Specifically, for a single bin, we show that the problem is solvable in pseudo-polynomial time and develop a polynomial time approximation scheme (PTAS) for general instances. For a natural subclass of instances we obtain a simpler scheme. This yields the first combinatorial PTAS for a non-trivial subclass of instances for 2DVP. For multiple bins, we develop a PTAS for a subclass of instances arising in the data placement problem. Finally, we show that when the number of distinct colors in the instance is fixed, our problem admits a PTAS, even if the items have arbitrary sizes and profits, and the bins are arbitrary.