Elsevier

Discrete Optimization

Volume 31, February 2019, Pages 103-114
Discrete Optimization

Trader multiflow and box-TDI systems in series–parallel graphs

https://doi.org/10.1016/j.disopt.2018.09.003Get rights and content
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Abstract

Series–parallel graphs are known to be precisely the graphs for which the standard linear systems describing the cut cone, the cycle cone, the T-join polytope, the cut polytope, the multicut polytope and the T-join dominant are TDI. We prove that these systems are actually box-TDI. As a byproduct, our result yields a min–max relation for a new problem: the trader multiflow problem. The latter generalizes both the maximum multiflow and min-cost multiflow problems and we show that it is polynomial-time solvable in series–parallel graphs.

MSC

90C27
90C57
05C70
05C85

Keywords

Box-TDI system
Series–parallel graph
Multiflow

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