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https://hdl.handle.net/10119/4916
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| Title: | On Geometric Structure of Global Roundings for Graphs and Range Spaces |
| Authors: | Asano, Tetsuo
Katoh, Naoki
Tamaki, Hisao
Tokuyama, Takeshi |
| Issue Date: | 2004 |
| Publisher: | Springer |
| Magazine name: | Lecture Notes in Computer Science |
| Volume: | 3111 |
| Start page: | 455 |
| End page: | 467 |
| Abstract: | 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. |
| Rights: | This is the author-created version of Springer, Tetsuo Asano, Naoki Katoh, Hisao Tamaki and Takeshi Tokuyama, Lecture Notes in Computer Science, 3111, 2004, 455-467. The original publication is available at www.springerlink.com, |
| URI: | https://hdl.handle.net/10119/4916 |
| Material Type: | author |
| Appears in Collections: | b10-1. 雑誌掲載論文 (Journal Articles)
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