Independence-System Realisations in Single-Source Unsplittable Flow
Additive-congestion constraints in single-source unsplittable flow can enforce stable-set structure.
Why am I seeing this Ranked on source trust — arXiv
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| Factor | Weight | Score | Contribution | Where it came from |
|---|---|---|---|---|
| Corroboration | 0.35 | 0.39 | +0.135 34% | 1 independent org on the story. Tier-3 aggregators never corroborate — they can show something is circulating, never that it is true. |
| Source trustleads | 0.25 | 0.85 | +0.212 53% | arXiv is the highest-trust source on this story and is first-party — the organisation announcing its own news. Trust is taken from the best source, not averaged. |
| Pickup rate | 0.20 | 0.00 | +0.000 0% | One counted organisation, so there is no spread to measure — nothing has picked this up to set a rate. |
| Freshness | 0.20 | 0.27 | +0.054 14% | Halves every 10 hours from the newest item on the story. This is the only factor that rewards a story for nothing more than being recent. |
Corroboration counts distinct organisations, once each, and only from tiers 1 and 2. Freshness halves every 10 hours, so this ranking is a snapshot and will differ at the next build.
What happened
Additive-congestion constraints in single-source unsplittable flow can enforce stable-set structure. This note isolates and generalises that mechanism. We introduce a path-closed notion of realising an independence system by the zero-cost choices of primary terminals in a directed acyclic flow instance. The definition quantifies over every directed source-terminal path and therefore remains valid under prefix borrowing, suffix splicing, and hybrid routes.Our main result extends the triangle mechanism: every finite loopless independence system has a polynomial-size realisation, measured in the incidence size of its minimal forbidden sets.
How this story arrived
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- 01 Arxivfirst-party first seen Independence-System Realisations in Single-Source Unsplittable Flow
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