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

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.