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{http://isa-afp.org/entries/Prpu_Maxflow.shtml},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Depends on: Flow_Networks