Summary
LetU 1,...,Un denote i.i.d. random variables with the uniform distribution on [0, 1]2, and letT 2≔T2(U1,...,Un) denote the shortest tour throughU 1,...,Un with square-weighted edges. By drawing on the quasi-additive structure ofT 2 and the boundary rooted dual process, it is shown that lim n→∞ E T 2(U 1,...,Un)= β for some finite constant β.
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This work was supported in part by NSF Grant DMS-9200656, Swiss National Foundation Grant 21-298333.90, and the US Army Research Office through the Mathematical Sciences Institute of Cornell University, whose assistance is gratefully acknowledged
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Yukich, J.E. Asymptotics for the Euclidean TSP with power weighted edges. Probab. Th. Rel. Fields 102, 203–220 (1995). https://doi.org/10.1007/BF01213389
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DOI: https://doi.org/10.1007/BF01213389
Mathematics Subject Classification (1990)
- 60D05
- 60F15
- 60C05