On the convergence of computational methods for the online bin stretching problem

TL;DR

This paper proves that computational methods for the online bin stretching problem do converge to the optimal solution and provides bounds on their performance gap, establishing a theoretical foundation for these approaches.

Contribution

It offers the first theoretical proof of convergence for computational methods in online bin stretching, along with bounds on their optimality gap.

Findings

Computational methods converge to the optimal solution.

Bounds on the gap to the optimal are established.

The results provide a theoretical foundation for these methods.

Abstract

Online bin stretching is an online packing problem where some of the best known lower and upper bounds were found through computational searches. The limiting factor in obtaining better bounds with such methods is the computational time allowed. However, there is still no theoretical guarantee that such methods do converge towards the optimal online performance. This paper shows that such methods do, in fact, converge; moreover, bounds on the gap to the optimal are also given. These results frame a theoretical foundation for the convergence of computational approaches for online problems.