English

Improved approximation bounds for Vector Bin Packing

Data Structures and Algorithms 2010-07-09 v1 Discrete Mathematics Optimization and Control

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 {\theta}(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.

Keywords

Cite

@article{arxiv.1007.1345,
  title  = {Improved approximation bounds for Vector Bin Packing},
  author = {Chetan S Rao and Jeffrey John Geevarghese and Karthik Rajan},
  journal= {arXiv preprint arXiv:1007.1345},
  year   = {2010}
}

Comments

15 pages, 3 algorithms

R2 v1 2026-06-21T15:45:55.520Z