Improved approximation bounds for Vector Bin Packing

TL;DR

This paper introduces an improved approximation scheme for the Vector Bin Packing problem, combining LP relaxation solutions with a greedy heuristic, achieving better guarantees especially in higher dimensions.

Contribution

It presents a new approximation algorithm that surpasses previous bounds for high-dimensional VBP and offers a 2-OPT scheme for specific input sets regardless of dimension.

Findings

Improved approximation bounds over previous methods for d > 2

Achieved a 2-OPT approximation scheme for certain inputs

Enhanced performance in high-dimensional vector bin packing

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.