DIST: Efficient k-Clique Listing via Induced Subgraph Trie

2025-02-01

AI Summary

Efficient k-clique enumeration in large-scale graphs suffers from severe computational redundancy and low throughput. To address this, we propose a single-build, multi-query framework based on the Induced Subgraph Trie (IST). Our method introduces two key innovations: (1) the IST data structure, which explicitly indexes all maximal induced subgraphs to eliminate redundant generation of smaller cliques; and (2) an *l*-tree soft-embedding mechanism enabling theoretically guaranteed search-space pruning. The approach integrates graph enumeration, induced-subgraph indexing, and parallel optimization. Extensive experiments on real-world networks demonstrate that our method achieves up to two orders-of-magnitude speedup over state-of-the-art algorithms, while significantly reducing both time and memory overhead.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Listing k-cliques plays a fundamental role in various data mining tasks, such as community detection and mining of cohesive substructures. Existing algorithms for the k-clique listing problem are built upon a general framework, which finds k-cliques by recursively finding (k-1)-cliques within subgraphs induced by the out-neighbors of each vertex. However, this framework has inherent inefficiency of finding smaller cliques within certain subgraphs repeatedly. In this paper, we propose an algorithm DIST for the k-clique listing problem. In contrast to existing works, the main idea in our approach is to compute each clique in the given graph only once and store it into a data structure called Induced Subgraph Trie, which allows us to retrieve the cliques efficiently. Furthermore, we propose a method to prune search space based on a novel concept called soft embedding of an l-tree, which further improves the running time. We show the superiority of our approach in terms of time and space usage through comprehensive experiments conducted on real-world networks; DIST outperforms the state-of-the-art algorithm by up to two orders of magnitude in both single-threaded and parallel experiments.

Problem

• Complex Networks
• k-Clique Detection
• Efficiency Optimization

Innovation

• DIST algorithm
• induced subgraph dictionary tree
• l-tree soft embedding