flow-network-builder

将优化问题建模为网络流问题

SKILL.md

--- frontmatter

name: flow-network-builder
description: Model optimization problems as network flow problems
allowed-tools:
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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

•Maximum Flow: Find max flow from source to sink
•Minimum Cut: Partition minimizing cut capacity
•Bipartite Matching: Maximum matching via flow
•Min-Cost Max-Flow: Cheapest maximum flow
•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": "array" },
    "source": { "type": "string" },
    "sink": { "type": "string" },
    "algorithm": { "type": "string" },
    "reduction": { "type": "string" }
  },
  "required": ["success"]
}