A Convex-Programming Approach for Efficient Directed Densest Subgraph Discovery
Bibliographic record
Abstract
Given a directed graph G, the directed densest subgraph (DDS) problem refers to finding a subgraph from G, whose density is the highest among all subgraphs of G. The DDS problem is fundamental to a wide range of applications, such as fake follower detection and community mining. Theoretically, the DDS problem closely connects to other essential graph problems, such as network flow and bipartite matching. However, existing DDS solutions suffer from efficiency and scalability issues. In this paper, we develop a convex-programming-based solution by transforming the DDS problem into a set of linear programs. Based on the duality of linear programs, we develop efficient exact and approximation algorithms. Especially, our approximation algorithm can support flexible parameterized approximation guarantees. We have performed an extensive empirical evaluation of our approaches on eight real large datasets. The results show that our proposed algorithms are up to five orders of magnitude faster than the state-of-the-art.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".