网络技术的传播
The Diffusion of Networking Technologies
摘要：
联网社区对互联网上联网技术升级的扩散所产生的级联效应的影响有着极大的兴趣。将全球互联网视为一个图，其中每个节点代表一个以经济为动机的互联网服务提供商（ISP），一个关键问题是确定可以触发级联的最小节点集，该级联导致图中的所有其他节点采用该协议。我们设计的第一个近似算法与可证明的性能保证这个问题，在一个模型中，捕捉以下关键问题：一个节点的决定升级应该受到影响的远程节点的决定，它希望与通信。给定一个互联网络G（V，E）和阈值函数θ，我们假设节点$u$在与G中活动节点的连通分量相邻时激活（升级到新技术），该连通分量的大小超过节点$u$的阈值θ（u）。我们的目标是选择可以激活图的其余部分的最小节点集。我们的主要贡献是基于线性规划的近似算法，我们补充计算硬度的结果和接近最佳的完整性差距。我们的算法，它不依赖于子模块优化技术，也突出了我们的问题和类似的问题研究的背景下，社交网络的算法之间的差异。
英文摘要：
There has been significant interest in the networking community on the impact of cascade effects on the diffusion of networking technology upgrades in the Internet. Thinking of the global Internet as a graph, where each node represents an economically-motivated Internet Service Provider (ISP), a key problem is to determine the smallest set of nodes that can trigger a cascade that causes every other node in the graph to adopt the protocol. We design the first approximation algorithm with a provable performance guarantee for this problem, in a model that captures the following key issue: a node's decision to upgrade should be influenced by the decisions of the remote nodes it wishes to communicate with. Given an internetwork G(V,E) and threshold function θ, we assume that node $u$ activates (upgrades to the new technology) when it is adjacent to a connected component of active nodes in G of size exceeding node $u$'s threshold θ(u). Our objective is to choose the smallest set of nodes that can cause the rest of the graph to activate. Our main contribution is an approximation algorithm based on linear programming, which we complement with computational hardness results and a near-optimum integrality gap. Our algorithm, which does not rely on submodular optimization techniques, also highlights the substantial algorithmic difference between our problem and similar questions studied in the context of social networks.
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