Clique is hard on average for regular resolution
Document typeConference report
PublisherAssociation for Computing Machinery (ACM)
Rights accessOpen Access
European Commission's projectAUTAR - A Unified Theory of Algorithmic Relaxations (EC-H2020-648276)
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.
CitationAtserias, A., Bonacina, I., Rezende, S., Lauria, M., Nordström, J., Razborov, A. Clique is hard on average for regular resolution. A: ACM Symposium on Theory of Computing. "Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing". New York: Association for Computing Machinery (ACM), 2018, p. 866-877.