Before revision:  By recent breakthrough work of Dey, Dubey and Molinaro (SODA, 2021), the bound on the integrality gap immediately implies that branch and bound requires n^{\operatorname{poly}(m)} time on random Gaussian IPs with good probability, which is polynomial when the number of constraints m is fixed  .
After revision:  By recent breakthrough work of Dey, Dubey and Molinaro (SODA, 2021), the bound on the integrality gap immediately implies that branch and bound requires n^{\operatorname{poly}(m)} time on random Gaussian IPs with good probability, which is polynomial when the number of constraints m is fixed . We derive this result via a novel meta-theorem, which relates the size of branch-and-bound trees and the integrality gap for random logconcave IPs .