Bibliographic record
Abstract
<title>Abstract</title> Graph analytics attract much attention from both research and industry communities. Due to its linear time complexity, the $k$-core decomposition is widely used in many real-world applications such as biology, social networks, community detection, ecology, and information spreading. In many such applications, the data graphs continuously change over time. The changes correspond to edge insertion and removal. Instead of recomputing the $k$-core, which is time-consuming, we study how to maintain the $k$-core efficiently. That is, when inserting or deleting an edge, we need to identify the affected vertices by searching for more vertices. The state-of-the-art order-based method maintains an order, the so-called $k$-order, among all vertices, which can significantly reduce the searching space. However, this order-based method is complicated to understand and implement, and its correctness is not formally discussed.In this work, we propose a simplified order-based approach by introducing the classical Order Data Structure to maintain the $k$-order, which significantly improves the worst-case time complexity for both edge insertion and removal algorithms. Also, our simplified method is intuitive to understand and implement; it is easy to argue the correctness formally. Additionally, we discuss a simplified batch insertion approach.The experiments evaluate our simplified method over 12 real and synthetic graphs with billions of vertices. Compared with the existing method, our simplified approach achieves high speedups up to 7.7x and 9.7x for edge insertion and removal, respectively.
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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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.015 | 0.006 |
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".