# Formalizing Push-Relabel Algorithms

 Title: Formalizing Push-Relabel Algorithms Authors: Peter Lammich and S. Reza Sefidgar Submission date: 2017-06-01 Abstract: We present a formalization of push-relabel algorithms for computing the maximum flow in a network. We start with Goldberg's et al.~generic push-relabel algorithm, for which we show correctness and the time complexity bound of O(V^2E). We then derive the relabel-to-front and FIFO implementation. Using stepwise refinement techniques, we derive an efficient verified implementation. Our formal proof of the abstract algorithms closely follows a standard textbook proof. It is accessible even without being an expert in Isabelle/HOL, the interactive theorem prover used for the formalization. BibTeX: @article{Prpu_Maxflow-AFP, author = {Peter Lammich and S. Reza Sefidgar}, title = {Formalizing Push-Relabel Algorithms}, journal = {Archive of Formal Proofs}, month = jun, year = 2017, note = {\url{https://isa-afp.org/entries/Prpu_Maxflow.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Flow_Networks Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.