Reduction to max-flow
Add super-source + super-sink. Handle lower bounds via 'demand' constraints. Check if super-source→super-sink flow saturates.
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Feasibility check
Max flow in reduced graph = sum of lower bounds → circulation exists.
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Min-cost circulation
Combined with costs. Solved via cycle-canceling or successive shortest paths.
Applications
Employee scheduling with min/max hours. Transportation with min/max on routes.