Formalizing the Edmonds-Karp Algorithm

 

Title: Formalizing the Edmonds-Karp Algorithm
Authors: Peter Lammich and S. Reza Sefidgar
Submission date: 2016-08-12
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.
BibTeX:
@article{EdmondsKarp_Maxflow-AFP,
  author  = {Peter Lammich and S. Reza Sefidgar},
  title   = {Formalizing the Edmonds-Karp Algorithm},
  journal = {Archive of Formal Proofs},
  month   = aug,
  year    = 2016,
  note    = {\url{http://isa-afp.org/entries/EdmondsKarp_Maxflow.shtml},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Depends on: Automatic_Refinement, DFS_Framework, Refine_Imperative_HOL, Refine_Monadic