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

{
  "type": "object",
  "properties": {
    "problemDescription": { "type": "string" },
    "problemType": {
      "type": "string",
      "enum": ["maxFlow", "minCut", "matching", "minCostFlow", "circulation"]
    },
    "constraints": { "type": "object" }
  },
  "required": ["problemDescription"]
}

Output Schema

{
  "type": "object",
  "properties": {
    "success": { "type": "boolean" },
    "networkDescription": { "type": "string" },
    "nodes": { "type": "array" },
    "edges": { "type": "array" },
    "source": { "type": "string" },
    "sink": { "type": "string" },
    "algorithm": { "type": "string" },
    "reduction": { "type": "string" }
  },
  "required": ["success"]
}