Approximation Algorithms for the Multiple Knapsack Problem with Assignment Restrictions

@article{Dawande2000ApproximationAF,
  title={Approximation Algorithms for the Multiple Knapsack Problem with Assignment Restrictions},
  author={Milind Dawande and Jayant Kalagnanam and Pınar Keskinocak and F. Sibel Salman and Ramamoorthi Ravi},
  journal={Journal of Combinatorial Optimization},
  year={2000},
  volume={4},
  pages={171-186}
}
Motivated by a real world application, we study the multiple knapsack problem with assignment restrictions (MKAR). We are given a set of items, each with a positive real weight, and a set of knapsacks, each with a positive real capacity. In addition, for each item a set of knapsacks that can hold that item is specified. In a feasible assignment of items to knapsacks, each item is assigned to at most one knapsack, assignment restrictions are satisfied, and knapsack capacities are not exceeded… 
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