What does this research mean for the field?

Novel approximation and exact algorithms utilizing graph reduction techniques can solve the anchored densest subgraph (ADS) problem up to four orders of magnitude faster than state-of-the-art methods while maintaining accuracy and providing strong theoretical guarantees. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to improve the discovery of anchored densest subgraphs with better efficiency and practical performance.

May 20, 2026

Efficient Anchored Densest Subgraph Discovery: Improved Time Complexity and Practical Performance

Key Points

The aim is to improve the discovery of anchored densest subgraphs with better efficiency and practical performance.
Proposed a novel approximation algorithm to reduce time complexity and maintain accuracy.
Introduced a graph reduction technique for localized ADS search while ensuring theoretical guarantees.
Developed an efficient exact algorithm to complement the approximation.
Proposed algorithms perform up to four orders of magnitude faster than existing state-of-the-art methods.

Abstract

Densest subgraph discovery (DSD) is a fundamental research topic in network science and graph databases. As a typical variant of DSD, the anchored densest subgraph (ADS) problem aims to detect a densest subgraph that is anchored around user-defined seed vertices. The ADS problem has been shown to be very useful in some personalized applications, such as community search and recommendation. While the ADS problem is very useful, existing algorithms suffer from weak theoretical guarantees and perform poorly in practice. To address these issues, we first propose a novel approximation algorithm with improved time complexity, achieving the same accuracy as existing methods while requiring significantly fewer iterations. To further enhance practical performance, we introduce a graph reduction technique that localizes the ADS search to a much smaller subgraph, while still providing non-trivial theoretical guarantees. Building on this approximation, we also develop an efficient exact algorithm. We have performed an extensive empirical evaluation of our approaches on 12 real large datasets. The results show that our proposed algorithms are up to four orders of magnitude faster than the state-of-the-art.

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