Optimisation of electrical network configuration: Complexity and algorithms for ring topologies

We consider power distribution networks containing source nodes producing electricity and representing consumers. These sources these consumers are interconnected by a switched network. Configuring this network consists in deciding which switches activated the orientation of links between switches, so as to obtain directed acyclic graph (DAG) from producer consumer nodes. This DAG is valid if electric flow it induces satisfies demand each without exceeding production capacity switch. show that problem such exists NP-complete. In case where exists, we study determining balances ratio amount produced maximum for source. minimization also NP-complete general but becomes polynomial ring topologies.