Bin Packing Problem: A Linear Constant-Space 3/2-Approximation Algorithm

TL;DR

This paper introduces a linear 3/2-approximation algorithm for the NP-hard Bin Packing Problem, achieving optimal theoretical bounds and outperforming existing algorithms in experiments.

Contribution

It presents the first linear-time algorithm with the best possible approximation ratio for BPP, combining theoretical optimality with practical efficiency.

Findings

Achieves the 3/2 approximation ratio in linear time

Outperforms previous approximation algorithms in experiments

Proves the algorithm's optimality under P≠NP

Abstract

Since the Bin Packing Problem (BPP) is one of the main NP-hard problems, a lot of approximation algorithms have been suggested for it. It has been proven that the best algorithm for BPP has the approximation ratio of 3/2 and the time order of O(n), unless P=NP. In the current paper, a linear 3/2-approximation algorithm is presented. The suggested algorithm not only has the best possible theoretical factors, approximation ratio, space order, and time order, but also outperforms the other approximation algorithms according to the experimental results, therefore, we are able to draw the conclusion that the algorithms is the best approximation algorithm which has been presented for the problem until now. Key words: Approximation Algorithm, Bin Packing Problem, Approximation Ratio, NP-hard.