License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITP.2021.25
URN: urn:nbn:de:0030-drops-139204
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13920/
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Lochbihler, Andreas

A Mechanized Proof of the Max-Flow Min-Cut Theorem for Countable Networks

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Abstract

Aharoni et al. [Ron Aharoni et al., 2010] proved the max-flow min-cut theorem for countable networks, namely that in every countable network with finite edge capacities, there exists a flow and a cut such that the flow saturates all outgoing edges of the cut and is zero on all incoming edges. In this paper, we formalize their proof in Isabelle/HOL and thereby identify and fix several problems with their proof. We also provide a simpler proof for networks where the total outgoing capacity of all vertices other than the source is finite. This proof is based on the max-flow min-cut theorem for finite networks.

BibTeX - Entry

@InProceedings{lochbihler:LIPIcs.ITP.2021.25,
  author =	{Lochbihler, Andreas},
  title =	{{A Mechanized Proof of the Max-Flow Min-Cut Theorem for Countable Networks}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{25:1--25:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13920},
  URN =		{urn:nbn:de:0030-drops-139204},
  doi =		{10.4230/LIPIcs.ITP.2021.25},
  annote =	{Keywords: flow network, optimization, infinite graph, Isabelle/HOL}
}

Keywords: flow network, optimization, infinite graph, Isabelle/HOL
Collection: 12th International Conference on Interactive Theorem Proving (ITP 2021)
Issue Date: 2021
Date of publication: 21.06.2021
Supplementary Material: The formalization is available in the Archive of Formal Proofs:
Software (Formalization): http://www.isa-afp.org/entries/MFMC_Countable.shtml

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