Bin Packing Problem: Two Approximation Algorithms

TL;DR

This paper introduces two approximation algorithms for the NP-hard Bin Packing Problem, achieving optimal theoretical bounds and improved practical efficiency through modifications and experimental validation.

Contribution

It presents a 3/2-approximation algorithm and a linear-time modification of FFD, enhancing both theoretical performance and practical efficiency.

Findings

The 3/2-approximation algorithm matches the best known theoretical ratio.

The modified FFD algorithm operates in linear time.

Experimental results confirm the efficiency of the proposed algorithms.

Abstract

The Bin Packing Problem is one of the most important optimization problems. In recent years, due to its NP-hard nature, several approximation algorithms have been presented. It is proved that the best algorithm for the Bin Packing Problem has the approximation ratio 3/2 and the time order O(n), unless P=NP. In this paper, first, a 3/2-approximation algorithm is presented, then a modification to FFD algorithm is proposed to decrease time order to linear. Finally, these suggested approximation algorithms are compared with some other approximation algorithms. The experimental results show the suggested algorithms perform efficiently. In summary, the main goal of the research is presenting methods which not only enjoy the best theoretical criteria, but also perform considerably efficient in practice.