Average-case complexity of a branch-and-bound algorithm for maximum independent set, under the $\mathcal{G}(n, p)$ random model

Average-case complexity of a branch-and-bound algorithm for max independent set, under the G(n, p) random model Abstract We study average-case complexity of branch-and-bound for max independent set in random graphs under the G(n, p) distribution. In this model every pair (u, v) of vertices belongs to E with probability p independently on the existence of any other edge. We make a precise case analysis, providing phase transitions between subexponential and exponential complexities depending on the probability p of the random model.