The Minimum Spanning Tree Constant in Geometrical Probability and Under the Independent Model; A Unified Approach
Name
OR-211-90.pdf
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809.38 KB
Format
Adobe PDF
Checksum (MD5)
4904089d9a0a441b935ada51ef615f67
Author(s)
Avram, Florin
Bertsimas, Dimitris J.
Date Issued
April 1990
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 211-90
Abstract
Given n uniformly and independently points in the d dimensional cube of unit volume, it is well established that the length of the minimum spanning tree on these n points is asymptotic to /3MsT(d)n(d-l)/d,where the constant PMST(d) depends only on the dimension d. It has been a major open problem to determine the constant 3MST(d). In this paper we obtain an exact expression of the constant MST(d) as a series expansion. Truncating the expansion after a finite number of terms yields a sequence of lower bounds; the first 3 terms give a lower bound which is already very close to the empirically estimated value of the constant. Our proof technique unifies the derivation for the MST asymptotic behavior for the Euclidean and the independent model.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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