Scalable Algorithm for Dynamic Quasi-clique Detection

2026-05-25

AI Summary

This work formally introduces the Dynamic Maximum Quasi-Clique Problem (DMQCP) and proposes DMI, an efficient maintenance framework for real-time dense subgraph mining in dynamic graph streams. DMI integrates an $l$-buffered $k$-MinHash scheme with Bottom-$k$ MinHash and incorporates a Neighbor Search-assisted Framework (NSF) to incrementally maintain high-quality quasi-clique candidates as the graph evolves. A batch reconstruction strategy is further employed to enhance solution stability. Experimental results demonstrate that DMI achieves up to four orders of magnitude speedup over static baselines on both real-world and synthetic datasets while preserving solution quality, thereby enabling scalable, real-time quasi-clique discovery in dynamic graphs.

Abstract

Identifying dense subgraphs known as quasi-cliques is pivotal in numerous graph mining tasks across domains such as social networks, biology, and e-commerce. While prior work has developed efficient algorithms for quasi-clique detection in static graphs, real-world networks are inherently dynamic, where edges appear and disappear continuously. This renders static methods inefficient and ill-suited for real-time analysis. In this paper, we initiate the study of the Dynamic Maximum Quasi-Clique Problem (DMQCP), which aims to maintain and update the largest quasi-clique in a graph under streaming graph updates. We propose DMI, a novel MinHash-based dynamic framework that supports fast, high-quality approximate maintenance of quasi-cliques. DMI leverages two update-efficient hashing schemes, i.e., $l$-buffered $k$-MinHash and Bottom-$k$ MinHash, to maintain candidate quasi-cliques incrementally. To ensure robustness and reduce bias, we further design a batch reconstruction strategy to periodically rebuild the candidate set, guaranteeing both stability and adaptability under frequent updates. Extensive experiments on real-world and synthetic datasets show that DMI achieves up to four orders of magnitude speedup over static baselines, while preserving solution quality. As a side product, we also propose a framework NSF that primarily uses the neighbor-search technique to maintain quasi-clique candidates while edge updating. This work establishes the first efficient algorithmic framework for dynamic quasi-clique extraction, enabling scalable and real-time dense subgraph mining in evolving networks.

Problem

• dynamic graph
• quasi-clique
• dense subgraph
• streaming updates
• real-time mining

Innovation

• Dynamic Quasi-clique
• MinHash
• Streaming Graph Updates
• Dense Subgraph Mining
• Incremental Maintenance