Clique Is Hard on Average for Regular Resolution

• We prove that for k ≫; 4√n regular resolution requires length nω(k) to establish that an ErdÅ's-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.

Ämnesord

NATURVETENSKAP  -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Computer Sciences (hsv//eng)

NATURVETENSKAP  -- Matematik -- Diskret matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Discrete Mathematics (hsv//eng)

Nyckelord

average complexity

clique

Resolution

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art (ämneskategori)

ref (ämneskategori)