Layer-Based Data Aggregation and Performance Analysis in Wireless Sensor Networks

Algorithm 2

Data aggregation tree construction.

Input: Graph 𝐺=(𝑉,𝐸);

Output: Data aggregation tree 𝑇=(𝑉^′,𝐸^′), the dominated set 𝐷_𝑖,𝑖=2,4,…, the set of connective nodes 𝐶_𝑖, 𝑖=1,3,…

(1) 𝑉^′=𝑉,   𝐸^′=∅;

(2) Breadth first search graph 𝐺 with the root as 𝑠;

(3) Divide all node of 𝑉^′ into layers 𝐿₀,𝐿₁,…,𝐿_𝑅;

(4) 𝐷₁={𝑠};

(5) for each node 𝑥∈𝐿₁, par(𝑥) = 𝑠; 𝐸^′=𝐸^′∪{(𝑥,𝑠)};

(6) for 𝑖 = 2 to 𝑅 do

(7)  calculate upper(𝑢), 𝑢∈𝐿_𝑖

(8)  if 𝑢𝑝𝑝𝑒𝑟(𝑢)=0 and 𝑢∈𝐿_𝑖, then 𝐿_𝑖=𝐿_𝑖/𝑢, 𝐿_𝑖+1=𝐿_𝑖+1∪{𝑢};

(9)  if 𝑖 is even, construct the layer independent set 𝐷_𝑖, and sequence the lower(𝑦) with decreasing order of the set size as

     𝑦₁,𝑦₂,…,𝑦∈𝐿_𝑖−1, and the set size as 𝑦₁,𝑦₂,…,𝑦∈𝐿_𝑖−1;

(10)  𝑗=1;

(11)  while 𝐿_𝑖 != empty do

(12)   for each node 𝑢∈ lower(𝑦_𝑗)

(13)     par(𝑢) = 𝑦_𝑗, 𝐸^′=𝐸^′∪𝑢,𝑦_𝑗, 𝐿_𝑖=𝐿_𝑖/𝑢;

(14)    if 𝑖 is even then 𝐶_𝑖=𝐶_𝑖∪𝑦_𝑗;

(15)   end for

(16)   𝑗=𝑗+1;

(17)  end while

(18) end for