The paper demonstrates a flaw in the algorithm presented in "A polynomial-time algorithm for 3-SAT" by Lizhi Du, which incorrectly identifies certain satisfiable 3-CNF boolean formulas as unsatisfiable.
The 3-FLIP algorithm, a local search algorithm for the Max-Cut problem, can have a superpolynomial smoothed runtime, in contrast to previous results showing efficient smoothed runtimes for other local search algorithms.