A unified approach to approximating resource allocation and scheduling
Journal of the ACM (JACM)
Improved Approximation Algorithms for Resource Allocation
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A quasi-PTAS for unsplittable flow on line graphs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Multicommodity demand flow in a tree and packing integer programs
ACM Transactions on Algorithms (TALG)
Energy efficient scheduling via partial shutdown
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Dependent Randomized Rounding via Exchange Properties of Combinatorial Structures
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Constrained non-monotone submodular maximization: offline and secretary algorithms
WINE'10 Proceedings of the 6th international conference on Internet and network economics
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We consider the problem of scheduling a set of resources over time. Each resource is specified by a set of time intervals (and the associated amount of resource available), and we can choose to schedule it in one of these intervals. The goal is to maximize the number of demands satisfied, where each demand is an interval with a starting and ending time, and a certain resource requirement. This problem arises naturally in many scenarios, e.g., the resource could be an energy source, and we would like to suitably combine different energy sources to satisfy as many demands as possible. We give a constant factor randomized approximation algorithm for this problem, under suitable assumptions (the so called no-bottleneck assumptions). We show that without these assumptions, the problem is as hard as the independent set problem. Our proof requires a novel configuration LP relaxation for this problem. The LP relaxation exploits the pattern of demand sharing that can occur across different resources.