Independence-System Realisations in Single-Source Unsplittable Flow
Read the original on arXiv AI →The paper introduces a path‑closed framework for realizing independence systems via zero‑cost choices of primary terminals in directed acyclic flow instances, extending the triangle mechanism to all finite loopless independence systems. It shows that such systems, including all finite simple graphs and hypergraph independence systems without singleton forbidden hyperedges, admit polynomial‑size realizations measured by the incidence size of minimal forbidden sets. The authors further specialize to odd cycles, deriving a rational family that yields a fractional cheap‑selection vector violating the odd‑cycle inequality and establishing an exact additive‑congestion threshold that approaches 1/2 for large cycles.
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