Analysis of the Harmonic Function Used in Bin-Packing

TL;DR

This paper explores a generalized harmonic function used in bin-packing algorithms, providing alternative proofs of its key properties and enhancing understanding of its role in approximation algorithms.

Contribution

It introduces a slight generalization of the harmonic function and offers new proofs of its fundamental properties, advancing theoretical understanding.

Findings

Generalized harmonic function with broader applicability

Alternative proofs of key properties of the harmonic function

Enhanced theoretical framework for bin-packing approximation algorithms

Abstract

The harmonic function was first introduced by Lee and Lee (JACM 1985) for analyzing their online bin-packing algorithm. Subsequently, it has been used to obtain approximation algorithms for many different packing problems. Here we slightly generalize the harmonic function and give alternative proofs of its important properties.