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

Authors:
Carlo Filippi;Alessandro Agnetis
Affiliations:
Department of Pure and Applied Mathematics, University of Padova, Via Belzoni 7, 35131, Padova, Italy;Department of Information Engineering, University of Siena, Via Roma 56, 53100, Siena, Italy
Venue:
Mathematical Programming: Series A and B
Year:
2005

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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.