An upper bound for the average length of the euclidean minimum spanning tree

Abstract

In this paper we estimate the average length of an Euclidean minimum spanning tree. If the vertices of an EMST are uniformly distributed on a unit disk in R ² we can derive the behavior of the edge lengths of the EMST constructed from these vertices by using the ordered statistics, and obtain an upper bound for the expected length of an EMST to be where n is the number of vertices of the EMST. This estimation is much closer to the actual values than the previous results. Experiment values are also given.

Keywords:

• EMST
• ETSP
• average case analysis
• ordered statistics
• poisson distribution

C.R.Categories:

• F.22