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FOLDER COMPLEXES AND MULTIFLOW COMBINATORIAL DUALITIES.
- Source :
-
SIAM Journal on Discrete Mathematics . 2011, Vol. 25 Issue 3/4, p1119-1143. 25p. 9 Diagrams. - Publication Year :
- 2011
-
Abstract
- In multiflow maximization problems, there are several combinatorial duality relations, such as the Ford-Fulkerson max-flow min-cut theorem for single commodity flows, Hu's max-biflow min-cut theorem for two-commodity flows, the 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, the μ-weighted maximum multiflow problem admits a combinatorial duality relation if and only if μ is represented by distances between certain subsets in a folder complex, and we 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 in the case of metric weights. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08954801
- Volume :
- 25
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 71525584
- Full Text :
- https://doi.org/10.1137/090767054