发表机构
Augusta University（奥古斯塔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出预测贪婪路由，利用带噪声的距离预测加速小世界网络中的去中心化消息传递，分别实现有坐标感知时的$O(\log n)$期望投递时间和无坐标感知时的$O(n)$期望投递时间，均优于Kleinberg经典$O(\log^2 n)$界限。
AI 中文摘要
小世界现象由Kleinberg给出了算法基础，他证明了在增强的$k$维晶格中，去中心化贪婪算法在$O(\log^2 n)$期望步数内传递消息。我们研究预测贪婪路由，其中转发消息的移动代理每一步移动到使带噪声的$(\varepsilon,\delta)$-预测距离目标距离最小的邻居，该预测每一步从以完整路由历史为条件的预言机重新抽取。根据该代理能观察到的内容，出现两种情况。具有坐标感知的代理仍能精确计算晶格距离，但无法计算捷径增强网络中的图距离，因为这取决于它尚未访问节点的捷径；给定图距离的$(\varepsilon,\delta)$-预测（经典模型从未提供的信息），它实现期望投递时间$O(\log n/(1-4k\varepsilon\delta))$，相对于$\Theta(\log^2 n)$是渐近改进。完全没有坐标感知的代理（隐私保护网络的自然模型，其节点从不披露坐标）甚至无法计算晶格距离；给定晶格距离的$(\varepsilon,\delta)$-预测，它仍能在$O(n/(1-4k\varepsilon\delta))$期望步数内到达目标。这些结果共同表明，适量正确类型的预测信息足以将去中心化路由加速到远低于Kleinberg经典界限，且即使节点完全不披露坐标，可靠投递仍可实现。
英文摘要
The small-world phenomenon was given an algorithmic foundation by Kleinberg, who showed that in an augmented $k$-dimensional lattice a decentralized greedy algorithm delivers a message in $O(\log^2 n)$ expected steps. We study predicted-greedy routing, in which a mobile agent forwarding the message moves at each step to the neighbor minimizing a noisy $(\varepsilon,δ)$-prediction of its distance to the target, redrawn at every step from an oracle conditioned on the full routing history. Two cases arise from what this agent can observe. An agent with the coordinate awareness can still compute lattice distance exactly, but not graph distance in the shortcut-augmented network, since that depends on the shortcuts of nodes it has not yet visited; given an $(\varepsilon,δ)$-prediction of graph distance, information the classical model never supplies, it achieves expected delivery time $O(\log n/(1-4k\varepsilonδ))$, an asymptotic improvement over $Θ(\log^2 n)$. An agent with no coordinate awareness at all, the natural model for a privacy-preserving network whose nodes never disclose their coordinates, cannot compute even lattice distance; given an $(\varepsilon,δ)$-prediction of lattice distance instead, it still reaches the target in $O(n/(1-4k\varepsilonδ))$ expected steps. Together these results show that a modest amount of predicted information, of the right kind, is enough to accelerate decentralized routing well below Kleinberg's classical bound, and that even when nodes reveal no coordinates at all, reliable delivery remains achievable.
