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

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