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Encyclopedia of Algorithms pp 1–6Cite as

Vector Bin Packing

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Years and Authors of Summarized Original Work

1976; Garey, Graham, Johnson, Yao

1977; Kou, Markowski

1977; Maruyama, Chang, Tang

1981; de la Vega, Lueker

1987; Yao

1990; Csirik, Frenk, Labbé, Zhang

1997; Woeginger

2001; Caprara, Toth

2004; Chekuri, Khanna

2009; Bansal, Caprara, Sviridenko

2010; Stillwell, Schanzenback, Vivien, Casanova

2011; Panigrahy, Talwar, Uyeda, Wieder

Problem Definition

In the vector bin packing problem, we are given an integral dimension d ≥ 1 and a list \(L = (x_{1},x_{2},\ldots ,x_{n})\) of items, where each item is a d-dimensional tuple x i = \((x_{i,1},x_{i,2},\ldots ,x_{i,d})\) with rational entries x i, j ∈ [0, 1]. The goal is to assign the items to a minimum number of multidimensional bins, where if X is the set of items assigned to a bin, we must have, for each j, 1 ≤ j ≤ d,

$$\displaystyle\sum _{x_{i}\in X}x_{i,j} \leq 1.$$

Note that when d = 1, the vector bin packing problem reduces to the classic (one-dimensional) bin packing problem.

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Recommended Reading

  1. Bansal N, Caprara A, Sviridenko M (2009) A new approximation method for set covering problems, with applications to multidimensional bin packing. SIAM J Comput 39:1256–1278

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Author information

Authors and Affiliations

  1. Department of Computer Science, Columbia University, New York, NY, USA

    David S. Johnson

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  1. David S. Johnson
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Correspondence to David S. Johnson .

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Editors and Affiliations

  1. Dept. Electrical Engineering & Computer Science, Northwestern University, Evanston, Illinois, USA

    Ming-Yang Kao

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Johnson, D.S. (2014). Vector Bin Packing. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-3-642-27848-8_495-1

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  • DOI: https://doi.org/10.1007/978-3-642-27848-8_495-1

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  • Publisher Name: Springer, Boston, MA

  • Online ISBN: 978-3-642-27848-8

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