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

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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.

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Authors and Affiliations

  1. Department of Pure and Applied Mathematics, University of Padova, Via Belzoni 7, 35131, Padova, Italy

    Carlo Filippi

  2. Department of Information Engineering, University of Siena, Via Roma 56, 53100, Siena, Italy

    Alessandro Agnetis

Authors
  1. Carlo Filippi
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  2. Alessandro Agnetis
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Correspondence to Carlo Filippi.

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Filippi, C., Agnetis, A. An asymptotically exact algorithm for the high-multiplicity bin packing problem. Math. Program. 104, 21–37 (2005). https://doi.org/10.1007/s10107-004-0567-y

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