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Asymptotics for the Euclidean TSP with power weighted edges
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  • Published: June 1995

Asymptotics for the Euclidean TSP with power weighted edges

  • J. E. Yukich1,2 

Probability Theory and Related Fields volume 102, pages 203–220 (1995)Cite this article

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  • 7 Citations

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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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References

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Authors and Affiliations

  1. Department of Mathematics, Lehigh University, 18015, Bethlehem, PA, USA

    J. E. Yukich

  2. Mathematical Sciences Institute, Cornell University, 409 College Avenue, 14850, Ithaca, NY, USA

    J. E. Yukich

Authors
  1. J. E. Yukich
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Additional information

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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  • Received: 24 August 1994

  • Revised: 23 December 1994

  • Issue Date: June 1995

  • DOI: https://doi.org/10.1007/BF01213389

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Mathematics Subject Classification (1990)

  • 60D05
  • 60F15
  • 60C05
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