genpark-dinics-max-flow-network-algorithm-skill

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SUMMARY

Dinic's blocking flow algorithm with level graphs and dead-end pruning for maximum network flow

README.md

Dinic's Max Flow Algorithm Skill

High-efficiency, zero-dependency Python implementation of Dinic's Maximum Flow Algorithm running in (O(V^2 E)) time.

Features

  • Level Graph Construction: BFS generates layered DAG structures to restrict search to shortest augmenting paths.
  • Blocking Flow Extraction: DFS pushes flow along active edges with dead-end pointer pruning.
  • Zero External Dependencies: Pure Python standard library.
  • Native MCP Protocol: JSON-RPC 2.0 stdio server compatible with Claude Desktop, Cursor, and Windsurf.

Architecture

graph LR
    Source["Source Node s"] --> BFS["BFS: Construct Level Graph"]
    BFS --> DFS["DFS: Push Blocking Flow along Layers"]
    DFS --> Check{"Sink Reachable in Residual Graph?"}
    Check -- Yes --> BFS
    Check -- No --> MaxFlow["Maximum Flow Achieved"]

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