A linear approximation algorithm for the BPP with the best possible absolute approximation ratio

TL;DR

This paper introduces a new linear approximation algorithm for the Bin Packing Problem that achieves the best possible approximation ratio of 3/2 with linear time complexity, improving the efficiency and optimality of solutions.

Contribution

It presents a novel approximation algorithm for BPP that attains the optimal ratio of 3/2 in linear time, matching theoretical bounds.

Findings

Achieves the best possible approximation ratio of 3/2.

Operates in linear time complexity O(n).

Proves the optimality of the approximation ratio under P≠NP.

Abstract

The Bin Packing Problem is one of the most important Combinatorial Optimization problems in optimization and has a lot of real-world applications. Many approximation algorithms have been presented for this problem because of its NP-hard nature. In this article also a new creative approximation algorithm is presented for this important problem. It has been proven that the best approximation ratio and the best time order for the Bin Packing Problem are 3/2 and O(n), respectively unless P=NP. The presented algorithm in this article has the best possible factors, O(n) and 3/2.