Bibliographic record
Abstract
Robust network design takes the very successful framework of robust optimization and applies it to the area of network design, motivated by applications in communication networks. The main premise is that demands across the network are not fixed, but are variable or uncertain. However, they are known to fall within a prescribed uncertainty set. Our solution must have sufficient capacity to route any demand in this set; moreover, the routing must be oblivious, meaning it must be fixed up front, and not depend on the particular choice of demand from within the uncertainty set. A particular choice of uncertainty set within this framework yields the "hose model", which has received particular attention due to applications to virtual private networks. A 2-approximation was known for the problem, using a solution template in the form of a tree. It was conjectured that this tree solution is actually always optimal; this became known as the "VPN Conjecture". As one of the central results of this thesis, we prove this conjecture in full generality. In addition, we demonstrate a counterexample to a stronger multipath (fractional routing) version of the conjecture which had also been proposed. We initiate a study of the robust network design problem more generally, with a focus on approximability. In the general model, where the uncertainty set is given by an arbitrary separable polyhedron, we give a strong inapproximability result. We then consider a new and natural model generalizing the symmetric hose model, based on demands routable on a given tree, and provide a constant factor approximation algorithm. Lastly, we compare oblivious routing with the much more flexible (but also less practical) dynamic routing scheme where the routing may vary depending on the demand pattern. We show that in the worst case, the cost of an optimal oblivious routing solution can be much more expensive than the dynamic optimum, by up to a logarithmic factor.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.020 | 0.005 |
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".