Construction of Quality Virtual Backbones with Link Fault Tolerance in Wireless Sensor Networks

Algorithm 4

Calculate -blocks.

Input: A 2 edge-connected graph , a colored subgraph of and , where .

Output: The set consisting of all 2E-blocks in .

1 Construct a BFS tree in , and let be the set of edges in . Let , .

2 for to do

3  Select a node with the smallest in .

4  ifthen

5  if is a white node then

6  Color blue, and .

7  end if

8  else

9  Let

10  for each edge do

11  Find a simple circle , whose edges are all in the edge set , and let be the set of all nodes in .

12  if there are no red nodes in then.

13  Let be the minimum ID of nodes in .

14  For each , let .

15  Color all nodes in red.

16  else

17  Let . Let and .

18  For each , .

19  Color all nodes in red.

20  for each do

21  For each node with , .

22  end for

23  end if

24  end for

25  .

26 end if

27 .

28 end for

29 Let and . Let

30 return.