Consider a complete graph on n vertices with edge weights chosen randomly and independently from e.g., 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 goes to infinity.
By: Bela Bollobas (Univ. of Memphis and Trinity College), David Gamarnik, Oliver Riordan (Trinity College), Benny Sudakov (Princeton Univ.)
Published in: RC21921 in 2000
LIMITED DISTRIBUTION NOTICE:
This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.
Questions about this service can be mailed to reports@us.ibm.com .