We prove that even in average case, the Euclidean Traveling Salesman Problem exhibits an integrality gap of $(1+\epsilon)$ for $\epsilon>0$ when the Held-Karp Linear Programming relaxation is augmented by all comb inequalities of bounded size. This implies that large classes of branch-and-cut algorithms take exponential time for the Euclidean TSP, even on random inputs.

翻译：我们证明,即使是在平均情况下,欧球旅行推销员问题也表明,当Alvad-Karp线性规划的放松因所有捆绑大小的梳式不平等而得到增强时,欧球旅行推销员问题就显示出整体差距为1美元(1 ⁇ epsilon) $(epsilon)>0美元($) 。 这意味着大型分支和切割算法对欧球旅游服务供应商来说需要指数化的时间,即使是随机输入。