Given an attributed graph $G$ and a query node $q$, \underline{C}ommunity \underline{S}earch over \underline{A}ttributed \underline{G}raphs (CS-AG) aims to find a structure- and attribute-cohesive subgraph from $G$ that contains $q$. Although CS-AG has been widely studied, they still face three challenges. (1) Exact methods based on graph traversal are time-consuming, especially for large graphs. Some tailored indices can improve efficiency, but introduce nonnegligible storage and maintenance overhead. (2) Approximate methods with a loose approximation ratio only provide a coarse-grained evaluation of a community's quality, rather than a reliable evaluation with an accuracy guarantee in runtime. (3) Attribute cohesiveness metrics often ignores the important correlation with the query node $q$. We formally define our CS-AG problem atop a $q$-centric attribute cohesiveness metric considering both textual and numerical attributes, for $k$-core model on homogeneous graphs. We show the problem is NP-hard. To solve it, we first propose an exact baseline with three pruning strategies. Then, we propose an index-free sampling-estimation-based method to quickly return an approximate community with an accuracy guarantee, in the form of a confidence interval. Once a good result satisfying a user-desired error bound is reached, we terminate it early. We extend it to heterogeneous graphs, $k$-truss model, and size-bounded CS. Comprehensive experimental studies on ten real-world datasets show its superiority, e.g., at least 1.54$\times$ (41.1$\times$ on average) faster in response time and a reliable relative error (within a user-specific error bound) of attribute cohesiveness is achieved.

翻译：给定属性图$G$和查询节点$q$，属性图上的社区搜索（CS-AG）旨在从$G$中找出一个包含$q$且结构属性兼具凝聚性的子图。尽管CS-AG已被广泛研究，但仍面临三个挑战：（1）基于图遍历的精确方法耗时，尤其在大图上；某些定制索引可提升效率，但会引入不可忽视的存储与维护开销。（2）近似比松散的近似方法仅提供社区质量的粗粒度评估，而非运行时具有精度保证的可靠评估。（3）属性凝聚性度量常忽略与查询节点$q$的重要相关性。我们基于面向$q$的属性凝聚性度量（同时考虑文本与数值属性），在同类图的$k$-核心模型上正式定义CS-AG问题，并证明该问题为NP难问题。为解决该问题，我们首先提出一种包含三种剪枝策略的精确基线方法。其次，我们提出一种无索引的基于采样与估计的方法，能以置信区间形式快速返回具有精度保证的近似社区。一旦结果满足用户期望的误差界，便提前终止。我们将该方法扩展至异构图、$k$-桁架模型及有界规模社区搜索。在十个真实数据集上的综合实验表明其优越性：例如响应速度至少快1.54倍（平均快41.1倍），且属性凝聚性可实现可靠相对误差（在用户指定误差界内）。