A Linear Approximation Algorithm for 2-Dimensional Vector Packing

TL;DR

This paper introduces a linear-time approximation algorithm for the 2-dimensional vector packing problem, improving efficiency while maintaining effective bin packing solutions.

Contribution

It presents a novel a}(n)-time approximation algorithm for 2D vector packing, inspired by previous quadratic algorithms, enhancing computational efficiency.

Findings

The algorithm operates in a}(n) time, significantly faster than previous methods.

It achieves near-optimal packing solutions within approximation bounds.

The approach is practical for large-scale bin packing applications.

Abstract

We study the 2-dimensional vector packing problem, which is a generalization of the classical bin packing problem where each item has 2 distinct weights and each bin has 2 corresponding capacities. The goal is to group items into minimum number of bins, without violating the bin capacity constraints. We propose a \Theta}(n)-time approximation algorithm that is inspired by the O(n^2) algorithm proposed by Chang, Hwang, and Park.