scholarly journals Efficiency of Linear Programming, Integer Programming and Minimal Spanning Tree for Network Model

2020 ◽  
Author(s):  
SANYAM GUPTA ◽  
Laxminarayan Das
Keyword(s):  
Linear Programming ◽  
Integer Programming ◽  
Network Model ◽  
Spanning Tree ◽  
Minimal Spanning Tree

DEVELOPING PROXIMITY GRAPHS BY PHYSARUM POLYCEPHALUM: DOES THE PLASMODIUM FOLLOW THE TOUSSAINT HIERARCHY?

2009 ◽  
Vol 19 (01) ◽  
pp. 105-127 ◽  
Author(s):  
ANDREW ADAMATZKY
Keyword(s):  
Foraging Behavior ◽  
Delaunay Triangulation ◽  
Spanning Tree ◽  
Physarum Polycephalum ◽  
Minimum Spanning Tree ◽  
Nearest Neighbour ◽  
Minimal Spanning Tree ◽  
Proximity Graphs ◽  
Relative Neighborhood Graph ◽  
Plasmodium Of Physarum Polycephalum

Plasmodium of Physarum polycephalum spans sources of nutrients and constructs varieties of protoplasmic networks during its foraging behavior. When the plasmodium is placed on a substrate populated with sources of nutrients, it spans the sources with protoplasmic network. The plasmodium optimizes the network to deliver efficiently the nutrients to all parts of its body. How exactly does the protoplasmic network unfold during the plasmodium's foraging behavior? What types of proximity graphs are approximated by the network? Does the plasmodium construct a minimal spanning tree first and then add additional protoplasmic veins to increase reliability and through-capacity of the network? We analyze a possibility that the plasmodium constructs a series of proximity graphs: nearest-neighbour graph (NNG), minimum spanning tree (MST), relative neighborhood graph (RNG), Gabriel graph (GG) and Delaunay triangulation (DT). The graphs can be arranged in the inclusion hierarchy (Toussaint hierarchy): NNG ⊆ MST ⊆ RNG ⊆ GG ⊆ DT . We aim to verify if graphs, where nodes are sources of nutrients and edges are protoplasmic tubes, appear in the development of the plasmodium in the order NNG → MST → RNG → GG → DT , corresponding to inclusion of the proximity graphs.

Minimal spanning tree subject to a side constraint

1982 ◽  
Vol 9 (4) ◽  
pp. 287-296 ◽  
Author(s):  
V. Aggarwal ◽  
Y.P. Aneja ◽  
K.P.K. Nair
Keyword(s):  
Spanning Tree ◽  
Minimal Spanning Tree ◽  
Side Constraint

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.

Literary writing style recognition via a minimal spanning tree-based approach

2016 ◽  
Vol 61 ◽  
pp. 145-153 ◽  
Author(s):  
Dmitry Shalymov ◽  
Oleg Granichin ◽  
Lev Klebanov ◽  
Zeev Volkovich
Keyword(s):  
Spanning Tree ◽  
Minimal Spanning Tree ◽  
Writing Style ◽  
Literary Writing
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