An O ( n log n ) Algorithm for Rectilinear Minimal Spanning Trees

1979 ◽  
Vol 26 (2) ◽  
pp. 177-182 ◽  
Author(s):  
F. K. Hwang
Keyword(s):  
Spanning Trees ◽  
Minimal Spanning Trees

On the number of leaves of a euclidean minimal spanning tree

1987 ◽  
Vol 24 (4) ◽  
pp. 809-826 ◽  
Author(s):  
J. Michael Steele ◽  
Lawrence A. Shepp ◽  
William F. Eddy
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Random Variables ◽  
Minimal Spanning Tree ◽  
Absolutely Continuous ◽  
Mean And Variance ◽  
Number Of Leaves ◽  
The Mean ◽  
Vertex Degrees ◽  
Minimal Spanning Trees

Let Vk,n be the number of vertices of degree k in the Euclidean minimal spanning tree of Xi, , where the Xi are independent, absolutely continuous random variables with values in Rd. It is proved that n–1Vk,n converges with probability 1 to a constant α k,d. Intermediate results provide information about how the vertex degrees of a minimal spanning tree change as points are added or deleted, about the decomposition of minimal spanning trees into probabilistically similar trees, and about the mean and variance of Vk,n.

Computing capacitated minimal spanning trees efficiently

Networks ◽  
1974 ◽  
Vol 4 (4) ◽  
pp. 299-310 ◽  
Author(s):  
A. Kershenbaum
Keyword(s):  
Spanning Trees ◽  
Minimal Spanning Trees

Depth functions and mutidimensional medians on minimal spanning trees

2019 ◽  
Vol 47 (2) ◽  
pp. 323-336
Author(s):  
Mengta Yang ◽  
Reza Modarres ◽  
Lingzhe Guo
Keyword(s):  
Spanning Trees ◽  
Depth Functions ◽  
Minimal Spanning Trees

On the number of leaves of a euclidean minimal spanning tree

1987 ◽  
Vol 24 (04) ◽  
pp. 809-826 ◽  
Author(s):  
J. Michael Steele ◽  
Lawrence A. Shepp ◽  
William F. Eddy
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Random Variables ◽  
Minimal Spanning Tree ◽  
Absolutely Continuous ◽  
Mean And Variance ◽  
Number Of Leaves ◽  
The Mean ◽  
Vertex Degrees ◽  
Minimal Spanning Trees

Let Vk,n be the number of vertices of degree k in the Euclidean minimal spanning tree of Xi , , where the Xi are independent, absolutely continuous random variables with values in Rd. It is proved that n –1 Vk,n converges with probability 1 to a constant α k,d. Intermediate results provide information about how the vertex degrees of a minimal spanning tree change as points are added or deleted, about the decomposition of minimal spanning trees into probabilistically similar trees, and about the mean and variance of Vk,n.

scholarly journals Image Phylogeny by Minimal Spanning Trees

2012 ◽  
Vol 7 (2) ◽  
pp. 774-788 ◽  
Author(s):  
Zanoni Dias ◽  
Anderson Rocha ◽  
Siome Goldenstein
Keyword(s):  
Spanning Trees ◽  
Minimal Spanning Trees

Finding minimal spanning trees in a euclidean coordinate space

1981 ◽  
Vol 21 (1) ◽  
pp. 46-54 ◽  
Author(s):  
O. Nevalainen ◽  
J. Ernvall ◽  
J. Katajainen
Keyword(s):  
Spanning Trees ◽  
Coordinate Space ◽  
Minimal Spanning Trees
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