发表机构
CNR-ISC, Rome, Italy（意大利罗马国家研究委员会信息系统研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究网络快速扩展下可达性与可搜索性的矛盾，提出算法无关的稀疏搜索成功率上界，并揭示几何尺度决定搜索有效性，实验验证了快速扩展网络中目标盲搜索的失效。
AI 中文摘要
路由和搜索对快速网络扩展的反应是相反的。短的图距离使得已知目的地易于到达，而在几步之内可访问的邻域可能远大于任何有限的检查预算。我们表明，这种张力对稀疏搜索施加了一个与算法无关的约束。如果$m_q$个相关节点在没有结构信息的情况下被放置在$N$个节点中，并且最多可以检查$M$个节点，那么任何目标盲探索协议的成功概率至多为$Mm_q/N$，无论连续检查之间的相关性、重访以及探索规则可能具有的任何结构偏好如何。几何结构决定了这一约束何时变得相关：当图距离球体积满足$V(R_c)\sim N/m_q$时，目标以阶一概率变得可访问。在这个尺度上，任何实现固定成功概率$\delta>0$的检查机制，必须相对于中性目标密度，将检查相关节点的概率至少丰富$N/(Mm_q)$阶。对于均匀搜索的候选集，这意味着可访问区域的可见部分趋于消失。因此，快速扩展的网络可以使稀有目标在几何上接近，而目标盲搜索仍然无效。在Krioukov双曲随机图和二维格点上的数值结果表明，在快速扩展的情况下，这种分离可以在仅几步之内出现，而格点的可访问性半径则代数增长。
英文摘要
Routing and search respond in opposite ways to rapid network expansion. Short graph distances make a known destination easy to reach, while the neighborhood accessible within a few hops can be vastly larger than any finite inspection budget. We show that this tension imposes an algorithm-independent constraint on sparse search. If $m_q$ relevant nodes are placed without structural information among $N$ nodes and at most $M$ nodes can be inspected, any target-blind exploration protocol has success probability at most $Mm_q/N$, irrespective of correlations between successive inspections, of revisits, and of any structural preference the exploration rule may have. Geometry determines when this constraint becomes relevant: a target becomes accessible with order-one probability when the graph-distance ball volume satisfies $V(R_c)\sim N/m_q$. At this scale, any inspection mechanism achieving a fixed success probability $δ>0$ must enrich the probability of inspecting relevant nodes by at least order $N/(Mm_q)$ relative to the neutral target density. For uniformly searched candidate sets, this entails a vanishing visible fraction of the accessible region. Thus rapidly expanding networks can make rare targets geometrically close while target-blind search remains ineffective. Numerical results on Krioukov hyperbolic random graphs and two-dimensional lattices show that this separation can arise within only a few hops in the rapidly expanding case, while the lattice accessibility radius grows algebraically.
Comments46 pages, 1 figure; includes supplementary material. Data and code: https://doi.org/10.5281/zenodo.22955225
