Abstract
We consider power distribution networks containing source nodes producing electricity and nodes representing electricity consumers interconnected by a switched network. Configuring this network consists in deciding which switches are activated and the orientation of the links between these switches, so as to obtain a directed graph from the producer nodes to the consumer nodes. This graph is valid if the electric flow it induces satisfies the demand of each consumer without exceeding the production capacity of each source and the flow capacity of each switch. We show that deciding if such a valid configuration exists is polynomial in a tree.
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