On Geometric Structure of Global Roundings for Graphs and Range Spaces
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概要
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Given a hypergraph H = (V,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 |Σ_<v∈F> (a(v)-α(v))| < 1 holds for each F ∈ 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 "shortest-path" axioms, and prove it for some special cases including some geometric range spaces and the shortest path hypergraph of a series-parallel graph.
- Springerの論文
- 2004-00-00
Springer | 論文
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