A new lower bound for classic online bin packing

TL;DR

This paper establishes a new, higher lower bound for the asymptotic competitive ratio of online bin packing algorithms, demonstrating the benefits of branching and adaptivity in lower bound proofs.

Contribution

It introduces a novel weight-based analysis method and proves a lower bound above 1.54278, surpassing previous bounds and highlighting new techniques in lower bound derivation.

Findings

Lower bound for online bin packing ratio is above 1.54278

Branching and full adaptivity are effective in lower bound proofs

New weight-based analysis method applied to classic problem

Abstract

We improve the lower bound on the asymptotic competitive ratio of any online algorithm for bin packing to above 1.54278. We demonstrate for the first time the advantage of branching and the applicability of full adaptivity in the design of lower bounds for the classic online bin packing problem. We apply a new method for weight based analysis, which is usually applied only in proofs of upper bounds. The values of previous lower bounds were approximately 1.5401 and 1.5403.