iBGP与约束连通性
iBGP and Constrained Connectivity
摘要：
我们发起的理论研究的问题，最大限度地减少在互联网上的自治系统（AS）的iBGP覆盖的大小受到来自标准的“热土豆”路由规则的正确性的自然概念。对于这两个自然版本的问题（我们测量的覆盖的大小，无论是边缘的数量或最大程度），我们证明了它是NP-难近似的一个因素比$Ω(\log n)$和提供近似算法的比率$\tilde{O}(\sqrt{n})$。此外，我们给出了一个稍差的$\tilde{O}(n^{2/3})$ -近似的原始对偶技术的基础上，具有快速和良好的实践中，我们通过模拟的实际拓扑结构的五个大型自治系统的优点。我们使用的主要技术是减少到一个新的基于连通性的网络设计问题，我们称之为约束连接。在这个问题中，我们给出一个图$G=(V,E)$，对于每对顶点$u,v \in V$，我们给出一个集合$S(u,v) \subseteq V$，称为该对的安全集。目标是找到$G$的最小子图$H$，其中每对顶点$u,v$都由$S(u,v)$中包含的路径连接。我们表明，iBGP问题可以减少到特殊情况下的约束连接$G = K_n$和安全集的几何定义的基础上的IGP距离在AS。我们还认为，约束连通性本身就是一个有趣的问题，因此在一般情况下提供更强的硬度结果（$2^{\log^{1-ε} n}$ -近似硬度）和完整性间隙（$n^{1/3 - ε}$）。在积极的一面，我们表明，约束连接原来是更简单的一些有趣的特殊情况下，比iBGP：当安全集是对称的和层次的，我们给出了一个多项式时间算法，计算最优解。
英文摘要：
We initiate the theoretical study of the problem of minimizing the size of an iBGP overlay in an Autonomous System (AS) in the Internet subject to a natural notion of correctness derived from the standard "hot-potato" routing rules. For both natural versions of the problem (where we measure the size of an overlay by either the number of edges or the maximum degree) we prove that it is NP-hard to approximate to a factor better than $Ω(\log n)$ and provide approximation algorithms with ratio $\tilde{O}(\sqrt{n})$. In addition, we give a slightly worse $\tilde{O}(n^{2/3})$-approximation based on primal-dual techniques that has the virtue of being both fast and good in practice, which we show via simulations on the actual topologies of five large Autonomous Systems. The main technique we use is a reduction to a new connectivity-based network design problem that we call Constrained Connectivity. In this problem we are given a graph $G=(V,E)$, and for every pair of vertices $u,v \in V$ we are given a set $S(u,v) \subseteq V$ called the safe set of the pair. The goal is to find the smallest subgraph $H$ of $G$ in which every pair of vertices $u,v$ is connected by a path contained in $S(u,v)$. We show that the iBGP problem can be reduced to the special case of Constrained Connectivity where $G = K_n$ and safe sets are defined geometrically based on the IGP distances in the AS. We also believe that Constrained Connectivity is an interesting problem in its own right, so provide stronger hardness results ($2^{\log^{1-ε} n}$-hardness of approximation) and integrality gaps ($n^{1/3 - ε}$) for the general case. On the positive side, we show that Constrained Connectivity turns out to be much simpler for some interesting special cases other than iBGP: when safe sets are symmetric and hierarchical, we give a polynomial time algorithm that computes an optimal solution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
