# 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}
}
• Published in SWAT 8 July 2004
• Mathematics
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…
2 Citations

### Recent Progress on Combinatorics and Algorithms for Low Discrepancy Roundings

The properties of low-discrepancy roundings are surveyed, especially, on the combinatorial properties of a global rounding whose discrepancy is less than 1.

### On Properties of a Set of Global Roundings Associated with Clique Connection of Graphs

• Mathematics
• 2004
Given a connected weighted graph G=(V,E), we consider a hypergraph H(G)=(V,F(G)) corresponding to the set of all shortest paths in G. For a given real assignment a on V satisfying 0≤a(v)≤1, a global

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