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View all- De Rezende SPotechin ARisse K(2023)Clique Is Hard on Average for Unary Sherali-Adams2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00008(12-25)Online publication date: 6-Nov-2023
Clique Is Hard on Average for Regular Resolution
Authors: 
Albert Atserias, 
Ilario Bonacina, Susanna F. De Rezende, Massimo Lauria, 
Jakob Nordström, Alexander RazborovAuthors Info & Claims
Albert Atserias, Ilario Bonacina, Susanna F. De Rezende, Massimo Lauria, Jakob Nordström, Alexander RazborovAuthors Info & ClaimsArticle No.: 23, Pages 1 - 26
Abstract
We prove that for k ≪ 4√n regular resolution requires length nΩ(k) to establish that an Erdős–Rényi graph with appropriately chosen edge density does not contain a k-clique. This lower bound is optimal up to the multiplicative constant in the exponent and also implies unconditional nΩ(k) lower bounds on running time for several state-of-the-art algorithms for finding maximum cliques in graphs.
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- Clique Is Hard on Average for Regular Resolution
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Publication History
Published: 30 June 2021
Accepted: 01 February 2021
Revised: 01 November 2020
Received: 01 March 2020
Published in JACM Volume 68, Issue 4
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- European Research Council under the European Union’s Horizon 2020 Research and Innovation Programme/ERC
- European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ ERC
- Swedish Research Council
- Russian Foundation for Basic Research
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View all- De Rezende SPotechin ARisse K(2023)Clique Is Hard on Average for Unary Sherali-Adams2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00008(12-25)Online publication date: 6-Nov-2023
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