Clique Is Hard on Average for Regular Resolution (Extended Abstract)

نویسندگان

  • Albert Atserias
  • Ilario Bonacina
  • Susanna F. de Rezende
  • Massimo Lauria
  • Jakob Nordström
  • Alexander Razborov
چکیده

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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تاریخ انتشار 2018