Consider a complete graph on n vertices with edge weights chosen randomly and independently from an exponential distribution with parameter 1. Fix k vertices and consider the minimum weight Steiner tree which contains these vertices. We prove that with high probability the weight of this tree is (1+o(1))(k-1)(log n-log k)/n when k =o(n) and n→∞.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
* Research supported in part by NSF grant DSM9971788
† Research supported in part by NSF grants DMS-0106589, CCR-9987845 and by the State of New Jersey. Part of this research was done while visiting IBM T. J. Watson Research Center.
Rights and permissions
About this article
Cite this article
Bollobás*, B., Gamarnik, D., Riordan, O. et al. On the Value of a Random Minimum Weight Steiner Tree. Combinatorica 24, 187–207 (2004). https://doi.org/10.1007/s00493-004-0013-z
Received:
Issue Date:
DOI: https://doi.org/10.1007/s00493-004-0013-z