### Abstract

We present a formalization of the Ford-Fulkerson method for computing the maximum flow in a network. Our formal proof closely follows a standard textbook proof, and is accessible even without being an expert in Isabelle/HOL--- the interactive theorem prover used for the formalization. We then use stepwise refinement to obtain the Edmonds-Karp algorithm, and formally prove a bound on its complexity. Further refinement yields a verified implementation, whose execution time compares well to an unverified reference implementation in Java. This entry is based on our ITP-2016 paper with the same title.

### License

BSD License

### Topics

- Computer science/Algorithms/Graph

### Session EdmondsKarp_Maxflow

- FordFulkerson_Algo
- EdmondsKarp_Termination_Abstract
- EdmondsKarp_Algo
- Augmenting_Path_BFS
- EdmondsKarp_Impl
- Edka_Checked_Impl
- Edka_Benchmark_Export

### Depends on

- Flow Networks and the Min-Cut-Max-Flow Theorem

### Used by

- A Formal Proof of the Max-Flow Min-Cut Theorem for Countable Networks

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## Cite

×

EdmondsKarp_Maxflow-AFP

    @article{EdmondsKarp_Maxflow-AFP,
      author  = {Peter Lammich and S. Reza Sefidgar},
      title   = {Formalizing the Edmonds-Karp Algorithm},
      journal = {Archive of Formal Proofs},
      month   = {August},
      year    = {2016},
      note    = {\url{https://isa-afp.org/entries/EdmondsKarp_Maxflow.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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