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| Title: | The structure and number of global roundings of a graph |
| Authors: | Asano, Tetsuo
Katoh, Naoki
Tamaki, Hisao
Tokuyama, Takeshi |
| Keywords: | Combinatorics
Rounding
Discrepancy
Graph
Hypergraph |
| Issue Date: | 2004-10-06 |
| Publisher: | Elsevier |
| Magazine name: | Theoretical Computer Science |
| Volume: | 325 |
| Number: | 3 |
| Start page: | 425 |
| End page: | 437 |
| DOI: | 10.1016/j.tcs.2004.02.044 |
| Abstract: | Given a connected weighted graph G=(V,E), we consider a hypergraph H_G=(V,P_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 rounding α with respect to H_G is a binary assignment satisfying that |∑_<v∈F>a(v)-α(v)|<1 for every F∈P_G. We conjecture that there are at most |V|+1 global roundings for H_G, and also the set of global roundings is an affine independent set. We give several positive evidences for the conjecture. |
| Rights: | NOTICE: This is the author’s version of a work accepted for publication by Elsevier.
Changes resulting from the publishing process, including peer review, editing, corrections,
structural formatting and other quality control mechanisms, may not be reflected in this
document. Changes may have been made to this work since it was submitted for publication.
A definitive version was subsequently published in Tetsuo Asano, Naoki Katoh, Hisao Tamaki and Takeshi Tokuyama, Theoretical Computer Science, 325(3), 2004, 425-437, http://dx.doi.org/10.1016/j.tcs.2004.02.044 |
| URI: | https://hdl.handle.net/10119/4897 |
| Material Type: | author |
| Appears in Collections: | b10-1. 雑誌掲載論文 (Journal Articles)
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