Generosity helps or an 11-competitive algorithm for three servers
Journal of Algorithms
Regular Article: ATX-Approach to Some Results on Cuts and Metrics
Advances in Applied Mathematics
Minimum 0-extensions of graph metrics
European Journal of Combinatorics
Regular Article: Graphs of Some CAT(0) Complexes
Advances in Applied Mathematics
A characterization of minimizable metrics in the multifacility location problem
European Journal of Combinatorics
The maximum multiflow problems with bounded fractionality
Proceedings of the forty-second ACM symposium on Theory of computing
Journal of Combinatorial Theory Series B
On duality and fractionality of multicommodity flows in directed networks
Discrete Optimization
On the fractionality of the path packing problem
Journal of Combinatorial Optimization
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In this paper, we give a complete characterization of the class of weighted maximum multiflow problems whose dual polyhedra have bounded fractionality. This is a common generalization of two fundamental results of Karzanov. The first one is a characterization of commodity graphs H for which the dual of maximum multiflow problem with respect to H has bounded fractionality, and the second one is a characterization of metrics d on terminals for which the dual of metric-weighed maximum multiflow problem has bounded fractionality. A key ingredient of the present paper is a nonmetric generalization of the tight span, which was originally introduced for metrics by Isbell and Dress. A theory of nonmetric tight spans provides a unified duality framework to the weighted maximum multiflow problems, and gives a unified interpretation of combinatorial dual solutions of several known min-max theorems in the multiflow theory.