On the Worst-case Performance of the Sum-of-Squares Algorithm for Bin Packing

TL;DR

This paper improves the theoretical worst-case performance bound of the Sum-of-Squares bin packing algorithm from 3 to approximately 2.78, advancing understanding of its efficiency in worst-case scenarios.

Contribution

It provides a tighter asymptotic worst-case performance bound for the Sum-of-Squares bin packing algorithm, refining previous results.

Findings

Worst-case performance ratio improved to 2.7777...

Enhances theoretical understanding of the algorithm's efficiency

Builds on prior bounds to provide a more precise analysis

Abstract

The Sum of Squares algorithm for bin packing was defined in [2] and studied in great detail in [1], where it was proved that its worst case performance ratio is at most 3. In this note, we improve the asymptotic worst case bound to 2.7777...