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"]
}