Formalizing the Edmonds-Karp algorithm. 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.
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References in zbMATH (referenced in 6 articles , 1 standard article )
Showing results 1 to 6 of 6.
- Doczkal, Christian; Pous, Damien: Graph theory in Coq: minors, treewidth, and isomorphisms (2020)
- Lammich, Peter: Efficient verified (UN)SAT certificate checking (2020)
- Lammich, Peter: Refinement to imperative HOL (2019)
- Lammich, Peter; Sefidgar, S. Reza: Formalizing network flow algorithms: a refinement approach in Isabelle/HOL (2019)
- Zhan, Bohua: Efficient verification of imperative programs using auto2 (2018)
- Lammich, Peter; Sefidgar, S. Reza: Formalizing the Edmonds-Karp algorithm (2016)