flow-network-builder

# Flow Network Builder Skill ## Purpose Model optimization problems as network flow problems, constructing appropriate flow networks and selecting optimal algorithms. ## Capabilities - Identify max-flow/min-cut modeling opportunities - Construct flow network from problem description - Select optimal flow algorithm - Handle min-cost flow variants - Bipartite matching reduction - Circulation problems ## Target Processes - advanced-graph-algorithms - graph-modeling - optimization problems ## Flow Problem Types 1. **Maximum Flow**: Find max flow from source to sink 2. **Minimum Cut**: Partition minimizing cut capacity 3. **Bipartite Matching**: Maximum matching via flow 4. **Min-Cost Max-Flow**: Cheapest maximum flow 5. **Circulation**: Flow with lower bounds ## Reduction Patterns - Assignment problems -> Bipartite matching - Scheduling -> Flow with constraints - Path cover -> Flow reduction - Edge-disjoint paths -> Unit capacity flow ## Input Schema ```json { "type": "object", "properties": { "problemDescription": { "type": "string" }, "problemType": { "type": "string", "enum": ["maxFlow", "minCut", "matching", "minCostFlow", "circulation"] }, "constraints": { "type": "object" } }, "required": ["problemDescription"] } ``` ## Output Schema ```json { "type": "object", "properties": { "success": { "type": "boolean" }, "networkDescription": { "type": "string" }, "nodes": { "type": "array" }, "edges": { "type": "ar...