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

Cornaz, Denis; Grappe, Roland; Lacroix, Mathieu (2019), Trader multiflow and box-TDI systems in series-parallel graphs, Discrete Optimization, 31, 1, p. 103-114. 10.1016/j.disopt.2018.09.003

Type
Article accepté pour publication ou publié
Date
2019
Journal name
Discrete Optimization
Volume
31
Number
1
Publisher
Elsevier
Pages
103-114
Publication identifier
Metadata
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Author(s)
Cornaz, Denis
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Grappe, Roland
Laboratoire d'Informatique de Paris-Nord [LIPN]
Lacroix, Mathieu cc
Laboratoire d'Informatique de Paris-Nord [LIPN]
Abstract (EN)
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.
Subjects / Keywords
Box-TDI system; Series–parallel graph; Multiflow