Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Resource allocation problems: algorithmic approaches
Resource allocation problems: algorithmic approaches
Approximate algorithms scheduling parallelizable tasks
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Disk load balancing for video-on-demand systems
Multimedia Systems
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)
A PTAS for the multiple knapsack problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for data placement on parallel disks
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Solving Multiple Knapsack Problems by Cutting Planes
SIAM Journal on Optimization
Polynominal time approximation schemes for class-constrained packing problem
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Approximation Schemes for Scheduling on Uniformly Related and Identical Parallel Machines
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Lecture notes on approximation algorithms: Volume I
Lecture notes on approximation algorithms: Volume I
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Polynominal time approximation schemes for class-constrained packing problem
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Almost optimal solutions for bin coloring problems
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Improved algorithms for data migration
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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We consider variants of the classic bin packing and multiple knapsack problems, in which sets of items of different classes (colors) need to be placed in bins; the items mayha ve different sizes and values. Each bin has a limited capacity, and a bound on the number of distinct classes of items it can hold. In the class-constrained multiple knapsack (CCMK) problem, our goal is to maximize the total value of packed items, whereas in the class-constrained bin-packing (CCBP), we seek to minimize the number of (identical) bins, needed for packing all the items. We give a polynomial time approximation scheme (PTAS) for CCMK and a dual PTAS for CCBP. We also show that the 0-1 class-constrained knapsack admits a fully polynomial time approximation scheme, even when the number of distinct colors of items depends on the input size. Finally, we introduce the generalized class-constrained packing problem (GCCP), where each item mayh ave more than one color. We show that GCCP is APX-hard, alreadyf or the case of a single knapsack, where all items have the same size and the same value. Our optimization problems have several important applications, including storage management for multimedia systems, production planning, and multiprocessor scheduling.