随机优先级前沿路由：针对c节点卡特尔的紧Θ(n^c)界
Random-Priority Frontier Routing: Tight $Θ(n^c)$ Bounds Against $c$-Node Cartels
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中文总结 AI 辅助
该研究针对可信节点网络中c节点卡特尔的路径规避问题，提出随机优先级前沿路由方法，证明其需Θ(n^c)次独立执行即可高概率避开卡特尔，得到紧的复杂度界。
中文摘要 AI 辅助
我们研究可信节点网络中的路径多样化问题，敏感信息通过中间节点中继，其中部分节点可能被攻陷。我们的随机路由规则为每个顶点分配独立随机优先级，并反复扩展已探索区域全局前沿上的最高优先级顶点。设G有n个顶点，s、t为诚实端点，C为c个被攻陷的中间节点组成的集合（称为卡特尔），删除C后s和t仍连通。对于每个固定的c和每个固定的目标概率q∈(0,1)，我们证明最坏情况下，Θ(n^c)次独立执行足以保证存在某条路径避开C的概率至少为q。
英文摘要
We study path diversification in trusted-node networks, where sensitive material is relayed through intermediate nodes, some of which may be compromised. Our randomized routing rule assigns each vertex an independent random priority and repeatedly expands the highest-priority vertex on the global frontier of the explored region. Let $G$ have $n$ vertices, let $s,t$ be honest endpoints, and let $C$ be a set of $c$ compromised intermediate vertices, called a cartel, whose deletion leaves $s$ and $t$ connected. For every fixed $c$ and every fixed target probability $q\in(0,1)$, we prove that $Θ(n^c)$ independent executions are sufficient in the worst case for some route to avoid $C$ with probability at least $q$.
发表机构
- Institute of Mathematics and Computer Science of the University of Latvia（拉脱维亚大学数学与计算机科学研究所）
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