  Let F be a uniformly distributed random k-SAT formula with n variables and m
clauses. We present a polynomial time algorithm that finds a satisfying
assignment of F with high probability for constraint densities
m/n<(1-eps_k)2^k\ln(k)/k, where eps_k->0. Previously no efficient algorithm was
known to find solutions with non-vanishing probability beyond m/n=1.817.2^k/k
[Frieze and Suen, J. of Algorithms 1996].
