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flow-network-builder

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Model optimization problems as network flow problems

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Source SKILL.md: https://github.com/a5c-ai/babysitter/blob/HEAD/library/specializations/algorithms-optimization/skills/flow-network-builder/SKILL.md

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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"]
}