Scalable Mining of Maximal Quasi-Cliques: An Algorithm-System Codesign Approach
Bibliographic record
Abstract
Given a user-specified minimum degree threshold $γ$, a $γ$-quasi-clique is a subgraph $g=(V_g,E_g)$ where each vertex $v\in V_g$ connects to at least $γ$ fraction of the other vertices (i.e., $\lceil γ\cdot(|V_g|-1)\rceil$ vertices) in $g$. Quasi-clique is one of the most natural definitions for dense structures useful in finding communities in social networks and discovering significant biomolecule structures and pathways. However, mining maximal quasi-cliques is notoriously expensive. In this paper, we design parallel algorithms for mining maximal quasi-cliques on G-thinker, a recent distributed framework targeting divide-and-conquer graph mining algorithms that decomposes the mining into compute-intensive tasks to fully utilize CPU cores. However, we found that directly using G-thinker results in the straggler problem due to (i) the drastic load imbalance among different tasks and (ii) the difficulty of predicting the task running time and the time growth with task-subgraph size. We address these challenges by redesigning G-thinker's execution engine to prioritize long-running tasks for mining, and by utilizing a novel timeout strategy to effectively decompose the mining workloads of long-running tasks to improve load balancing. While this system redesign applies to many other expensive dense subgraph mining problems, this paper verifies the idea by adapting the state-of-the-art quasi-clique algorithm, Quick, to our redesigned G-thinker. We improve Quick by integrating new pruning rules, and fixing some missed boundary cases that could lead to missed results. Extensive experiments verify that our new solution scales well with the number of CPU cores, achieving 201$\times$ runtime speedup when mining a graph with 3.77M vertices and 16.5M edges in a 16-node cluster.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".