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Node-Capacitated Ring Routing

2002
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Mathematics of Operations Research
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We consider the node-capacitated routing problem in an undirected ring network along with its fractional relaxation, the node-capacitated multicommodity flow problem. For the feasibility problem, Farkas' lemma provides a characterization for general undirected graphs asserting roughly that there exists such a flow if and only if the so-called distance inequality holds for every choice of distance functions arising from non-negative node-weigths. For rings this (straightforward) result will be

doi:10.1287/moor.27.2.372.323
fatcat:th6tfb7mevdr3ekkbd57gape44