Scalable Community Search with Accuracy Guarantee on Attributed Graphs

TL;DR

This work addresses the scalable Community Search over Attributed Graphs (CS-AG) problem, which seeks a connected $k$-core containing a query node while optimizing a $q$-centric attribute distance that combines textual and numerical attributes. It proves NP-hardness and delivers two complementary solutions: an exact baseline with three pruning strategies and an index-free sampling-estimation method that provides a runtime confidence interval guarantee on the attribute cohesiveness via Bag of Little Bootstrap and Hoeffding-based sampling. The approximate method can early-terminate when a user-specified relative error bound is met and extends to heterogeneous graphs, size-bounded settings, and alternative community models. Extensive experiments on ten real-world datasets show substantial speedups (often orders of magnitude) and reliable accuracy, validating the practicality of the approach for large-scale attributed graphs.

Abstract

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.

Figures (10)

• Figure 1: An example of CS: (a) A snapshot of IMDB with attributes at the bottom. (b)-(e) Different results of four methods.
• Figure 2: An example of $k$-core and connected $k$-core
• Figure 3: A search tree for the $\tilde{H}_2$ in Figure \ref{['fig:kcore']} (c)
• Figure 4: The pipeline of our sampling-estimation method
• Figure 5: Effectiveness (a)-(b) and efficiency (c)-(d) results over homogeneous graphs

Theorems & Definitions (23)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Theorem 1
• Theorem 2
• Lemma 1
• Theorem 3
• Example 1
• Theorem 4