Journal Article10.1023/A:1009894503716
Approximation Algorithms for the Multiple Knapsack Problem with Assignment Restrictions
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TL;DR: This work studies the multiple knapsack problem with assignment restrictions (MKAR) and shows that simple greedy approaches yield 1/3-approximation algorithms for the objective of maximizing assigned weight, and gives an (1/3,2)-approximating algorithm for the bicriteria problem of minimizing utilized capacity.
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Abstract: 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. We consider the objectives of maximizing assigned weight and minimizing utilized capacity.
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Citations
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