Bibliographic record
Abstract
$ \newcommand{\nba}{\text{nba}} \newcommand{\np}{\textsf{NP}} $ While the maximum single-sink unsplittable and confluent flow problems have been studied extensively, algorithmic work has been primarily restricted to the case where one imposes the no-bottleneck assumption $(\nba)$ (that the maximum demand $d_{\max}$ is at most the minimum capacity $u_{\min}$). For instance, under the $\nba$ there is a factor-$4.43$ approximation algorithm due to Dinitz et al. (1999) for the unsplittable flow problem. Under the even stronger assumption of uniform capacities, there is a factor-$3$ approximation algorithm due to Chen et al. (2007) for the confluent flow problem. We show, however, that unlike the unsplittable flow problem, a constant-factor approximation algorithm cannot be obtained for the single-sink confluent flow problem even with the no-bottleneck assumption. Specifically, we prove that it is $\np$-hard to approximate single-sink confluent flow to within $O(\log^{1-\epsilon}(n))$, for any $\epsilon> 0$. The remainder of our results focus upon the setting without the no-bottleneck assumption. Using exponential-size demands, Azar and Regev prove a $\Omega(m^{1-\epsilon})$ inapproximability result for maximum cardinality single-sink unsplittable flow in directed graphs. We prove that this lower bound applies to undirected graphs, including planar networks (and for confluent flow). This is the first super-constant hardness known for undirected single-sink unsplittable flow. Furthermore, we show $\Omega(m^{1/2-\epsilon})$-hardness even if all demands and capacities lie within an arbitrarily small range $[1,1+\Delta]$, for $\Delta > 0$. This result is sharp in that if $\Delta=0$, then it becomes a single-sink maximum edge-disjoint paths problem which can be solved exactly via a maximum flow algorithm. This motivates us to study maximum priority flows for which we show the same inapproximability bound.
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.
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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 0.001 |
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".