Scheduling Multiprocessor Tasks to Minimize Schedule Length
IEEE Transactions on Computers
Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Complexity of scheduling parallel task systems
SIAM Journal on Discrete Mathematics
Approximate algorithms scheduling parallelizable tasks
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
Improved approximations of packing and covering problems
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Algorithmic Chernoff-Hoeffding inequalities in integer programming
Random Structures & Algorithms
Tight approximations for resource constrained scheduling and bin packing
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Efficient approximation algorithms for scheduling malleable tasks
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Scheduling malleable and nonmalleable parallel tasks
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Journal of the ACM (JACM)
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SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
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SIAM Journal on Optimization
Preemptive Scheduling on Dedicated Processors: Applications of Fractional Graph Coloring
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Preemptive Parallel Task Scheduling in O(n)+Poly(m) Time
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
A New Fully Polynomial Approximation Scheme for the Knapsack Problem
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
The round-up property of the fractional chromatic number for proper circular arc graphs
Journal of Graph Theory
Scheduling Malleable Parallel Tasks: An Asymptotic Fully Polynomial-Time Approximation Scheme
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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Approximating the Advertisement Placement Problem
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BROADNETS '04 Proceedings of the First International Conference on Broadband Networks
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A scheduling framework for UWB & cellular networks
Mobile Networks and Applications - Special issue: Recent advances in wireless networking
Approximation algorithms for mixed fractional packing and covering problems
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Independence and coloring problems on intersection graphs of disks
Efficient Approximation and Online Algorithms
Approximation algorithms for min-max and max-min resource sharing problems, and applications
Efficient Approximation and Online Algorithms
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International Journal of Automation and Computing
Fast asymptotic FPTAS for packing fragmentable items with costs
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
An approximation algorithm for the general mixed packing and covering problem
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
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We study resource constrained scheduling problems where the objective is to compute feasible preemptive schedules minimizing the makespan and using no more resources than what are available. We present approximation schemes along with some inapproximibility results showing how the approximability of the problem changes in terms of the number of resources. The results are based on linear programming formulations (though with exponentially many variables) and some interesting connections between resource constrained scheduling and (multidimensional, multiple-choice, and cardinality constrained) variants of the classical knapsack problem. In order to prove the results we generalize a method by Grigoriadis et al. for the max-min resource sharing problem to the case with weak approximate block solvers (i.e. with only constant, logarithmic, or even worse approximation ratios). Finally we present applications of the above results in fractional graph coloring and multiprocessor task scheduling.