Maximum Flow and Minimum Cut Workbench

How to use Maximum Flow and Minimum Cut Workbench

Breadth-first residual augmentations send flow from source to sink. Once no residual path remains, reachable vertices define a cut. Every arc capacity, intermediate-node balance and equality of flow/cut values is checked before export.

1. Enter node labels json, arc json (from, to, capacity), source label, sink label.
2. Choose the stated convention and check the units and supported model.
3. Calculate, inspect the result, then copy or download it.

Good to know

• Exact-grid inputs are plain decimals with at most six places and magnitude≤1e9. Raw JSON number spelling is checked before conversion; decimal strings can preserve exact grid values. Exact rational intermediates are bounded to 8192 bits.2–30 vertices, 150 unique directed arcs and 10000 augmentations. Antiparallel arcs are distinct; self-loops and duplicate directed arcs are refused. Capacities share one unit. No real network control, capacity prediction or minimum-cost objective.
• Local calculation only; no input persistence or external lookup. Text/JSON is limited to 30000 characters and output to 1000000 characters. Numeric model inputs and precision/work limits are stated on this page. Approximate JSON numbers retain full stored values; exact arithmetic outputs retain decimal or fraction strings. Unsupported states fail explicitly.