The Satisfiability Threshold of Random 3-SAT Is at Least 3.52

MohammadTaghi Hajiaghayi, Gregory B. Sorkin

Published 2003-10-13, updated 2003-10-22Version 2

We prove that a random 3-SAT instance with clause-to-variable density less than 3.52 is satisfiable with high probability. The proof comes through an algorithm which selects (and sets) a variable depending on its degree and that of its complement.