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Pferschy, “The multiple subset sum problem,” Technical Report 12/1998, Faculty of Economics, University of Graz, 1998.Ĭ. Sudan, “Improved low degree testing and its applications,” in Proc. Orlin, Network Flows, Prentice Hall: New Jersey, 1993. For the bicriteria problem of minimizing utilized capacity subject to a minimum requirement on assigned weight, we give an (1/3,2)-approximation algorithm.Ī.K. We give two different 1/2-approximation algorithms: the first one solves single knapsack problems successively and the second one is based on rounding the LP relaxation solution. We show that simple greedy approaches yield 1/3-approximation algorithms for the objective of maximizing assigned weight. We focus on obtaining approximate solutions in polynomial computational time. We consider the objectives of maximizing assigned weight and minimizing utilized capacity. 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. In addition, for each item a set of knapsacks that can hold that item is specified. We are given a set of items, each with a positive real weight, and a set of knapsacks, each with a positive real capacity.

Motivated by a real world application, we study the multiple knapsack problem with assignment restrictions (MKAR).

Knapsack approximation algorithm