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Documents authored by Engström, David


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Track A: Algorithms, Complexity and Games
Average-Case Hardness of Binary-Encoded Clique in Proof and Communication Complexity

Authors: Susanna F. de Rezende, David Engström, Yassine Ghannane, Duri Andrea Janett, and Artur Riazanov

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)


Abstract
We study the average-case hardness of establishing that a graph does not have a large clique in both proof and communication complexity. We show exponential lower bounds on the length of cutting planes and bounded-depth resolution over parities refutations of the binary encoding of clique formulas on randomly sampled dense graphs. Moreover, we show that the randomized communication complexity of finding a falsified clause in these formulas is polynomial.

Cite as

Susanna F. de Rezende, David Engström, Yassine Ghannane, Duri Andrea Janett, and Artur Riazanov. Average-Case Hardness of Binary-Encoded Clique in Proof and Communication Complexity. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 151:1-151:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{derezende_et_al:LIPIcs.ICALP.2026.151,
  author =	{de Rezende, Susanna F. and Engstr\"{o}m, David and Ghannane, Yassine and Janett, Duri Andrea and Riazanov, Artur},
  title =	{{Average-Case Hardness of Binary-Encoded Clique in Proof and Communication Complexity}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{151:1--151:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.151},
  URN =		{urn:nbn:de:0030-drops-265407},
  doi =		{10.4230/LIPIcs.ICALP.2026.151},
  annote =	{Keywords: proof complexity, communication complexity, cutting planes, bounded-depth resolution over parities, clique problem, average-case hardness, binary encoding}
}
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