Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Approximation algorithms for partial covering problems
Journal of Algorithms
Saving an epsilon: a 2-approximation for the k-MST problem in graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Approximating the k-multicut problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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)
Primal-dual schema for capacitated covering problems
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Contact center scheduling with strict resource requirements
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Minimum Cost Resource Allocation for Meeting Job Requirements
IPDPS '11 Proceedings of the 2011 IEEE International Parallel & Distributed Processing Symposium
A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
On column-restricted and priority covering integer programs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
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We consider the problem of allocating resources to satisfy demand requirements varying over time. The input specifies a demand for each timeslot. Each resource is specified by a start-time, end-time, an associated cost and a capacity. A feasible solution is a multiset of resources such that at any point of time, the sum of the capacities offered by the resources is at least the demand requirement at that point of time. The goal is to minimize the total cost of the resources included in the solution. This problem arises naturally in many scenarios such as workforce management, sensor networks, cloud computing, energy management and distributed computing. We study this problem under the partial cover setting and the zero-one setting. In the former scenario, the input also includes a number k and the goal is to choose a minimum cost solution that satisfies the demand requirements of at least k timeslots. For this problem, we present a 16-approximation algorithm; we show that there exist "well-structured" near-optimal solutions and that such a solution can be found in polynomial time via dynamic programming. In the zero-one setting, a feasible solution is allowed to pick at most one copy of any resource. For this case, we present a 4-approximation algorithm; our algorithm uses a novel LP relaxation involving flow-cover inequalities.