The Construction of a Virtual Backbone with a Bounded Diameter in a Wireless Network

Algorithm 2: -GOC-SCBDAS.

Input: An SCDG

Output: An SCBDAS

1 color all nodes in white.

2 use a leader selection algorithm to select a node to be a root node, and color black and all nodes ingray.

3 build a BFS tree of with root by searching out-neighbors of each node.

4 , , and.

5 .

6 let , and set.

7 for every even do

8 determine one MIBDAS of by using a greedy algorithm based on the weight function, where is the subgraph induced by .

   .

9 end

10 set , color the nodes in gray and the nodes in black.

11.

12 while} do

13 find a node with the maximum weight function in , color it black, and color each node of gray.

14 end

15 for each pair of nodes with , add each node in the shortest path from to to.

16 .

17 return.

Algorithm 2: -GOC-SCBDAS.