graph-algorithm-selector

# 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 ```json { "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" }, "...