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The travelling salesman constant (Beardwood–Halton–Hammersley)

Narrow the constant β in the length β√n of the shortest tour through n random points, rigorously between 0.6277 and 0.8810.

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1{
2 "domain": "mathematics",
3 "topics": [
4 "probability",
5 "computational-geometry"
6 ],
7 "type": "proof",
8 "source": {
9 "key": "optimization-constants",
10 "name": "Optimization Constants in Mathematics",
11 "url": "https://teorth.github.io/optimizationproblems/constants/12a.html",
12 "id": "12",
13 "curator": "Terence Tao and contributors",
14 "status": "open",
15 "as_of": "2026-10-20",
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17 }
18}