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genpark-push-relabel-fifo-max-flow-skill

mcp
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SUMMARY

Goldberg-Tarjan Push-Relabel maximum flow algorithm with FIFO vertex discharge and height relabeling

README.md

Push-Relabel Max Flow Algorithm Skill

Robust, zero-dependency Python implementation of the Goldberg-Tarjan Push-Relabel Algorithm for asymptotic (O(V^3)) maximum flow computation.

Features

  • Preflow-Push Dynamics: Operates locally by pushing excess flow across downhill residual edges.
  • Height Function Relabeling: Maintains valid labeling bounds ensuring no augmenting path exists when excess dissipates.
  • 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 TD
    NodeU["Vertex u with Excess Flow e(u) > 0"] --> CheckHeight{"Height h(u) == h(v) + 1?"}
    CheckHeight -- Yes --> Push["Push delta = min(e(u), c_f(u, v))"]
    CheckHeight -- No --> Relabel["Relabel: h(u) = 1 + min h(v)"]

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