AI 中文总结
研究植入子图检测在信息受限（通过有限非自适应边查询）时的问题，推导查询复杂度的信息论下界与算法上界，所提算法利用三种结构机制，为几类植入图建立匹配界，推广了现有相关结果。
AI 中文摘要
植入子图检测问题是判断随机图中是否包含隐藏的结构化子图。经典形式下是观察整个邻接矩阵来区分埃尔德什 - 雷尼随机图和在其内部植入规定图副本得到的图。本文研究信息受限版本，植入结构是任意图序列\(\Gamma = (\Gamma_n)_{n\geq1}\)，观察者只能通过有限数量的非自适应边查询获取信息。我们研究可靠检测所需的最小查询复杂度，推导了查询复杂度的信息论下界和算法上界，所提算法利用三种结构机制，还为几类植入图建立了匹配界。
英文摘要
The planted subgraph detection problem asks whether a random graph contains a hidden structured subgraph. In the classical formulation, the entire adjacency matrix is observed and one distinguishes between an Erdős--Rényi random graph and one obtained by planting a copy of a prescribed graph inside an Erdős--Rényi random graph. The statistical and computational limits of this problem under full observation are now well understood, even for arbitrary planted subgraphs. In this paper, we investigate an information-limited version of the problem in which the planted structure is an arbitrary sequence of graphs $Γ=(Γ_n)_{n\geq1}$, where $Γ_n$ is embedded in an ambient graph on $n$ vertices, but the observer does not have access to the full adjacency matrix. Instead, information is acquired through a limited number of non-adaptive edge queries. We study the minimum query complexity required for reliable detection. We derive general information-theoretic lower bounds and complementary algorithmic upper bounds on the query complexity as functions of the query budget and structural properties of the planted graph. The proposed algorithms exploit three distinct structural mechanisms: dense local motifs, high-degree vertices, and global edge density. We establish matching bounds, up to polylogarithmic factors, for several broad families of planted graphs, including clique-like, bounded-cover, and hub-dominated graph classes. Our framework substantially generalizes existing query-complexity results for planted clique and planted dense subgraph models, providing a unified treatment of arbitrary planted subgraphs under restricted graph access.
