Deterministic Independent Sets in the Semi-Streaming Model
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We consider the independent set problem in the semi-streaming model. For any input graph G = (V, E) with n vertices, an independent set is a set of vertices with no edges between any two elements. In the semi-streaming model, G is presented as a stream of edges and any algorithm must use Õ(n) bits of memory to output a large independent set at the end of the stream. Prior work has designed various semi-streaming algorithms for finding independent sets. Due to the hardness of finding maximum and maximal independent sets in the semi-streaming model, the focus has primarily been on finding independent sets in terms of certain parameters, such as the maximum degree Δ. In particular, there is a simple randomized algorithm that obtains independent sets of size n/(Δ+1) in expectation, which can also be achieved with high probability using more complicated algorithms. For deterministic algorithms, the best bounds are significantly weaker. The best we know is a straightforward algorithm that finds an Ω̃(n/(Δ²)) size independent set. We show that this straightforward algorithm is nearly optimal by proving that any deterministic semi-streaming algorithm can only output an Õ(n/(Δ²)) size independent set. Our result proves a strong separation between the power of deterministic and randomized semi-streaming algorithms for the independent set problem.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.007 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.002 | 0.000 |
| Open science | 0.006 | 0.005 |
| Research integrity | 0.000 | 0.004 |
| 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