Half-integrality of node-capacitated multiflows and tree-shaped facility locations on trees
- Hiroshi Hirai
- Math. Program.
This paper is an exposition of a unified approach to multiflow problems using certain polyhedral objects called tight spans or TX-spaces. The tight span was introduced by Isbell and Dress, independent on the multiflow research. In the middle of 90’s, Karzanov and Chepoi explored the significance of tight spans in the multiflow theory. We explain how the tight span derives min-max relations to multiflow problems and how its geometry affects discreteness issues of flows and potentials.