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The Cartographer
Comb inequalities for typical Euclidean TSP instances
December 01, 2020 Β· Declared Dead Β· π arXiv.org
"No code URL or promise found in abstract"
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Authors
Wesley Pegden, Anish Sevekari
arXiv ID
2012.00292
Category
cs.DS: Data Structures & Algorithms
Cross-listed
cs.DM,
math.CO,
math.PR
Citations
3
Venue
arXiv.org
Last Checked
4 months ago
Abstract
We prove that even in average case, the Euclidean Traveling Salesman Problem exhibits an integrality gap of $(1+Ξ΅)$ for $Ξ΅>0$ 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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