1 research outputs found
Super Strong ETH is False for Random -SAT
It has been hypothesized that -SAT is hard to solve for randomly chosen
instances near the "critical threshold", where the clause-to-variable ratio is
. Feige's hypothesis for -SAT says that for all
sufficiently large clause-to-variable ratios, random -SAT cannot be refuted
in polynomial time. It has also been hypothesized that the worst-case -SAT
problem cannot be solved in time, as multiple known
algorithmic paradigms (backtracking, local search and the polynomial method)
only yield an time algorithm. This hypothesis has been called
the "Super-Strong ETH", modeled after the ETH and the Strong ETH.
Our main result is a randomized algorithm which refutes the Super-Strong ETH
for the case of random -SAT, for any clause-to-variable ratio. Given any
random -SAT instance with variables and clauses, our algorithm
decides satisfiability for in time, with high
probability. It turns out that a well-known algorithm from the literature on
SAT algorithms does the job: the PPZ algorithm of Paturi, Pudlak, and Zane
(1998).Comment: 15 page