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arXiv · 1007.1345

Improved approximation bounds for Vector Bin Packing

Chetan S Rao·Jeffrey John Geevarghese·Karthik Rajan
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Abstract

In this paper we propose an improved approximation scheme for the Vector Bin Packing problem (VBP), based on the combination of (near-)optimal solution of the Linear Programming (LP) relaxation and a greedy (modified first-fit) heuristic. The Vector Bin Packing problem of higher dimension (d \geq 2) is not known to have asymptotic polynomial-time approximation schemes (unless P = NP). Our algorithm improves over the previously-known guarantee of (ln d + 1 + epsilon) by Bansal et al. [1] for higher dimensions (d > 2). We provide a θ(1) approximation scheme for certain set of inputs for any dimension d. More precisely, we provide a 2-OPT algorithm, a result which is irrespective of the number of dimensions d.

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Chetan S Rao, Jeffrey John Geevarghese, Karthik Rajan. 2010-07-08. Improved approximation bounds for Vector Bin Packing. https://arxiv.org/abs/1007.1345

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