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The Minimum Spanning Tree Constant in Geometrical Probability and Under the Independent Model; A Unified Approach

Author(s)
Avram, Florin; Bertsimas, Dimitris J.
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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.
Date issued
1990-04
URI
http://hdl.handle.net/1721.1/5189
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 211-90

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