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DOI: 10.4230/LIPIcs.ITP.2023.3

A Formal Analysis of RANKING

Authors: Mohammad Abdulaziz and Christoph Madlener

Published in: LIPIcs, Volume 268, 14th International Conference on Interactive Theorem Proving (ITP 2023)

Abstract

We describe a formal correctness proof of RANKING, an online algorithm for online bipartite matching. An outcome of our formalisation is that it shows that there is a gap in all combinatorial proofs of the algorithm. Filling that gap constituted the majority of the effort which went into this work. This is despite the algorithm being one of the most studied algorithms and a central result in theoretical computer science. This gap is an example of difficulties in formalising graphical arguments which are ubiquitous in the theory of computing.

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Mohammad Abdulaziz and Christoph Madlener. A Formal Analysis of RANKING. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{abdulaziz_et_al:LIPIcs.ITP.2023.3,
  author =	{Abdulaziz, Mohammad and Madlener, Christoph},
  title =	{{A Formal Analysis of RANKING}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{3:1--3:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-284-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{268},
  editor =	{Naumowicz, Adam and Thiemann, Ren\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.3},
  URN =		{urn:nbn:de:0030-drops-183785},
  doi =		{10.4230/LIPIcs.ITP.2023.3},
  annote =	{Keywords: Matching Theory, Formalized Mathematics, Online Algorithms}
}

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A Formal Analysis of RANKING

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