On Geometric Structure of Global Roundings for Graphs and Range Spaces

@inproceedings{Asano2004OnGS,
  title={On Geometric Structure of Global Roundings for Graphs and Range Spaces},
  author={Tetsuo Asano and Naoki Katoh and Hisao Tamaki and Takeshi Tokuyama},
  booktitle={SWAT},
  year={2004}
}
Given a hypergraph \(\mathcal{H} = (V, \mathcal{F})\) and a [0,1]-valued vector a ∈ [0,1] V , its global rounding is a binary (i.e.,{0,1}-valued) vector α ∈ {0,1} V such that |∑ v ∈ F (a(v) − α(v))|< 1 holds for each \(F \in \mathcal{F}\). We study geometric (or combinatorial) structure of the set of global roundings of a using the notion of compatible set with respect to the discrepancy distance. We conjecture that the set of global roundings forms a simplex if the hypergraph satisfies… 

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