Comb inequalities for typical Euclidean TSP instances

12/01/2020

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by   Wesley Pegden, et al.

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We prove that even in average case, the Euclidean Traveling Salesman Problem exhibits an integrality gap of (1+ϵ) for ϵ>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.