  A recently proposed exact algorithm for the maximum independent set problem
is analyzed. The typical running time is improved exponentially in some
parameter regions compared to simple binary search. The algorithm also
overcomes the core transition point, where the conventional leaf removal
algorithm fails, and works up to the replica symmetry breaking (RSB) transition
point. This suggests that a leaf removal core itself is not enough for typical
hardness in the random maximum independent set problem, providing further
evidence for RSB being the obstacle for algorithms in general.
