Graph Algorithm Selector Skill

Purpose

Select the optimal graph algorithm based on problem constraints, graph properties, and performance requirements.

Capabilities

• Constraint analysis for algorithm selection
• Trade-off analysis (Dijkstra vs Bellman-Ford vs Floyd-Warshall)
• Special case detection (sparse vs dense, negative edges)
• Algorithm complexity mapping to constraints
• Suggest algorithm variants and optimizations

Target Processes

• shortest-path-algorithms
• advanced-graph-algorithms
• graph-traversal
• graph-modeling

Algorithm Selection Matrix

Shortest Path

Scenario	Algorithm	Complexity
Unweighted	BFS	O(V+E)
Non-negative weights	Dijkstra	O((V+E)log V)
Negative weights	Bellman-Ford	O(VE)
All pairs	Floyd-Warshall	O(V^3)
DAG	Topological + DP	O(V+E)

MST

Scenario	Algorithm	Complexity
Sparse graph	Kruskal	O(E log E)
Dense graph	Prim	O(V^2) or O(E log V)

Input Schema

{
  "type": "object",
  "properties": {
    "problemType": {
      "type": "string",
      "enum": ["shortestPath", "mst", "connectivity", "flow", "matching", "traversal"]
    },
    "graphProperties": { "type": "object" },
    "constraints": {
      "type": "object",
      "properties": {
        "V": { "type": "integer" },
        "E": { "type": "integer" },
        "negativeWeights": { "type": "boolean" },
        "negativeCycles": { "type": "boolean" }
      }
    }
  },
  "required": ["problemType", "constraints"]
}

Output Schema

{
  "type": "object",
  "properties": {
    "success": { "type": "boolean" },
    "recommendedAlgorithm": { "type": "string" },
    "complexity": { "type": "string" },
    "alternatives": { "type": "array" },
    "reasoning": { "type": "string" }
  },
  "required": ["success", "recommendedAlgorithm"]
}