外平面网络的VPN树路由猜想
The VPN Tree Routing Conjecture for Outerplanar Networks
摘要：
VPN树路由猜想是关于虚拟专用网设计问题的一个猜想。它指出，对称版本的问题总是有一个最优解，具有树状结构。在最近的工作中，Hurkens、Keijande和Stougie（Proc. IPCO XI，2005; SIAM J. Discrete Math.，2007年）已经证明，当网络是一个环时，该猜想成立。几个月前，Grandoni、Kaibel、Oriolo和Skutella发现了一个关于环的VPN猜想的较短证明（将出现在Oper上）。Res. Lett.，2008年）。在他们的论文中，Grandoni等人介绍了另一个猜想，称为金字塔路由猜想（或简称PR猜想），这意味着VPN猜想。在这里，我们考虑PR猜想的一个加强版本。首先，我们建立了几个通用的工具，可以适用于任意网络。然后利用它们证明了外平面网络满足PR猜想。
英文摘要：
The VPN Tree Routing Conjecture is a conjecture about the Virtual Private Network Design problem. It states that the symmetric version of the problem always has an optimum solution which has a tree-like structure. In recent work, Hurkens, Keijsper and Stougie (Proc. IPCO XI, 2005; SIAM J. Discrete Math., 2007) have shown that the conjecture holds when the network is a ring. A shorter proof of the VPN Conjecture for rings was found a few months ago by Grandoni, Kaibel, Oriolo and Skutella (to appear in Oper. Res. Lett., 2008). In their paper, Grandoni et al. introduce another conjecture, called the Pyramidal Routing Conjecture (or simply PR Conjecture), which implies the VPN Conjecture. Here we consider a strengthened version of the PR Conjecture. First we establish several general tools which can be applied in arbitrary networks. Then we use them to prove that outerplanar networks satisfy the PR Conjecture.
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