A Short Proof of the VPN Tree Routing Conjecture on Ring Networks

TL;DR

This paper provides a concise proof of a stronger version of the VPN Tree Routing Conjecture specifically for ring networks, potentially aiding in proving the conjecture for more general network types.

Contribution

It introduces a shorter proof of a stronger conjecture related to VPN tree routing on ring networks, simplifying previous complex proofs.

Findings

Proof of a stronger conjecture for ring networks

Simplified proof technique based on linear programming duality

Potential implications for general network VPN routing conjecture

Abstract

The VPN Tree Routing Conjecture states that there always exists an optimal solution to the symmetric Virtual Private Network Design (sVPND) problem where the paths between all terminals form a tree. Only recently, Hurkens, Keijsper, and Stougie gave a proof of this conjecture for the special case of ring networks. Their proof is based on a dual pair of linear programs and is somewhat in- volved. We present a short proof of a slightly stronger conjecture which might also turn out to be useful for proving the VPN Tree Routing Conjecture for general networks.