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RIMS-1675 Folder complexes and multiflow combinatorial dualities
| Content Provider | Semantic Scholar |
|---|---|
| Author | Hirai, Hiroshi |
| Copyright Year | 2009 |
| Abstract | In multiflow maximization problems, there are several combinatorial duality relations, such as Ford-Fulkerson’s max-flow min-cut theorem for single commodity flows, Hu’s max-biflow min-cut theorem for two-commodity flows, Lovász-Cherkassky duality theorem for free multiflows, and so on. In this paper, we provide a unified framework for such multiflow combinatorial dualities by using the notion of a folder complex, which is a certain 2-dimensional polyhedral complex introduced by Chepoi. We show that for a nonnegative weight μ on terminal set, μ-weighted maximum multiflow problem admits a combinatorial duality relation if and only if μ is represented by distances among certain subsets in a folder complex, and show that the corresponding combinatorial dual problem is a discrete location problem on the graph of the folder complex. This extends a result of Karzanov for the case of metric weights. Also we give a special optimality criterion to such combinatorial dual problems and give a characterization of such weights in terms of the combinatorial dimension. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.kurims.kyoto-u.ac.jp/preprint/file/RIMS1675.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
