An online bin-packing problem with an underlying ternary structure

TL;DR

This paper investigates an online bin-packing problem with items arriving in double-packs, employing the kernel method to analyze the ternary random walk structure underlying the enumeration process.

Contribution

It introduces a novel online bin-packing model with double-pack arrivals and applies the kernel method to analyze its enumeration, extending Kn"odel's original idea.

Findings

Analysis of the ternary random walk structure

Application of the kernel method to enumeration

Insights into dual problem with small items

Abstract

Following an orginal idea by Kn\"odel, an online bin-packing problem is considered where the the large items arrive in double-packs. The dual problem where the small items arrive in double-packs is also considered. The enumerations have a ternary random walk flavour, and for the enumeration, the kernel method is employed.