Rule of Thumb

When the diameter increases from 2x to (2x+ß), with ß(>0) small at will, the number of optimal nodes suddently grows since the optimal value increases from x to (x+1).
   


Figure 1
   
Optimal nodes are placed in general within a circle around the center of the network. Let us suppose the presence of a node, say N, placed exactly in the center of the MANET. Its value is x. Since N distance is (x-ε) from dense MANET boundary, with ε>=0, only nodes placed within a distance of ε from N will value x.
   


Figure 2
   
Now suppose that node N (placed in the center of the network) is (x+ß) distant from the dense MANET boundary, with ß>0. This suddently changes its value from x to (x+1). All nodes (x+1-ε), with ε>0, far from most distant network nodes will weigh (x+1). Consequently, they all will be optimal. These nodes are placed in a circle of radius (1-ß-ε) around N.
   
In conclusion, when the dense MANET diameter changes from 2x to (2x+ß), the number of optimal nodes greatly increases.