A note on the ring loading problem

TL;DR

This paper improves bounds on converting split routing solutions to unsplittable solutions in the Ring Loading Problem, a key issue in optical network routing, and disproves a longstanding conjecture.

Contribution

It provides a tighter bound for load increase during routing conversion and refutes a well-known conjecture in the field.

Findings

Converted split routing to unsplittable with at most +19/14 D load increase

Established an improved lower bound of +1.1 D on the load increase

Disproved a famous conjecture by Schrijver et al.

Abstract

The Ring Loading Problem is an optimal routing problem arising in the planning of optical communication networks which use bidirectional SONET rings. In mathematical terms, it is an unsplittable multicommodity flow problem on undirected ring networks. We prove that any split routing solution to the Ring Loading Problem can be turned into an unsplittable solution while increasing the load on any edge of the ring by no more than +(19/14)D, where D is the maximum demand value. This improves upon a classical result of Schrijver, Seymour, and Winkler (1998) who obtained a slightly larger bound of +(3/2)D. We also present an improved lower bound of +1.1 D (previously +1.01 D) on the best possible bound and disprove a famous long-standing conjecture of Schrijver et al. in this context.