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arXiv · 2012.00292

Comb inequalities for typical Euclidean TSP instances

Wesley Pegden·Anish Sevekari
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Abstract

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.

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Wesley Pegden, Anish Sevekari. 2023-03-30. Comb inequalities for typical Euclidean TSP instances. https://arxiv.org/abs/2012.00292

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