# 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{https://isa-afp.org/entries/EdmondsKarp_Maxflow.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Flow_Networks Used by: MFMC_Countable