The bin packing problem consists of finding the minimum number of bins, of given capacity D, required to pack a set of objects, each having a certain weight. We consider the high-multiplicity version of the problem, in which there are only C different weight values. We show that when C = 2 the problem can be solved in time O(log D). For the general case, we give an algorithm which provides a solution requiring at most C − 2 bins more than the optimal solution, i.e., an algorithm that is asymptotically exact. For fixed C, the complexity of the algorithm is O(poly(log D)), where poly(·) is a polynomial function not depending on C.

Filippi, C., Agnetis, A. (2005). An asymptotically exact algorithm for the high-multiplicity bin packing problem. MATHEMATICAL PROGRAMMING, 104, 21-37.

### An asymptotically exact algorithm for the high-multiplicity bin packing problem

#### Abstract

The bin packing problem consists of finding the minimum number of bins, of given capacity D, required to pack a set of objects, each having a certain weight. We consider the high-multiplicity version of the problem, in which there are only C different weight values. We show that when C = 2 the problem can be solved in time O(log D). For the general case, we give an algorithm which provides a solution requiring at most C − 2 bins more than the optimal solution, i.e., an algorithm that is asymptotically exact. For fixed C, the complexity of the algorithm is O(poly(log D)), where poly(·) is a polynomial function not depending on C.
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Filippi, C., Agnetis, A. (2005). An asymptotically exact algorithm for the high-multiplicity bin packing problem. MATHEMATICAL PROGRAMMING, 104, 21-37.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11365/17816`