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

Algorithm 1

: GOC-SCDAS.

Input: An SCDG

Output: An SCDAS

1 select a node as a root node through a leader selection algorithm.

2 .

3 construct a new digraph , where .

4 .

5 .

6 return .

7 subroutine .

8 color all nodes in white, and let denote all white nodes.

9 construct a BFS tree of rooted at by searching out-neighbors of each node.

10 color black and each node in gray.

11 .

12 let represent the shortest path length from to in the BFS tree .

13 let , and be the maximum value of .

14 for do

15 find a dominating set of using a greedy algorithm based on the weight function , where denotes the subgraph induced by .

16 end

17 .

18 color the nodes in black, color the nodes in gray.

19 .

20 .

21 whiledo

22 find a node in , color it black, and color all nodes in gray.

23 .

24 .

25 end

26 .

27 let .

28 for to do

29 for do

30  suppose that is the parent of with the largest .

31  suppose that is the parent of with the largest .

32  color and black.

33  .

34 end

35 for do

36  if there is not one black node in parent nodes then

37   choose one parent node with the largest and color black.

38   .

39  end

40 end

41 end

42 return