K-clique and k-cycle counting in the streaming model
Why this work is in the frame
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Bibliographic record
Abstract
In this thesis, we give algorithms for two graph problems: k -clique (Kk) and k-cycle (Ck) counting in the streaming model. The streaming model is a computational model to solve problems on large sequential data sets. Compared to the conventional computational model, the streaming model requires efficient space and small time per item. The input of the problems is the number of vertices n v, for a given graph G, constants epsilon', delta> 0, an integer k isin; (0, nv), and a sequential set of edges of G in "an arbitrary order. The algorithm reduces the counting problems to Frequency Moment problems using a sketch over alpha - stable random variables for alpha isin; (1,1.9] and pseudorandom generators. Our algorithm is based on Indyk's technique. Indyk claims his technique is provably correct for general alpha other than 1 or 2 but he does not aware any practical applications [16]. This thesis shows that k-clique (Kk) and k-cycle (C k) counting are such applications involving general alpha isin; (1,1.9]. Our algorithm achieves space efficiency when k is small and the density of Kk or C k in G is large.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it