International Scholarly Research Notices

Research Article

A New TDMA Scheduling Algorithm for Data Collection over Tree-Based Routing in Wireless Sensor Networks

Algorithm 1

The colouring algorithm.
Input:
o r i g i n a l g r a p h G = ( V , E )
c o n fl i c t g r a p h G C = ( V C , E C )
V C = V = { 𝑣 1 , 𝑣 2 , … , 𝑣 𝑁 }
Output: { ( 𝑣 1 , 𝑐 1 ) , ( 𝑐 2 , 𝑐 2 ) , … , ( 𝑣 𝑁 , 𝑐 𝑁 ) }
𝐢 𝑖 ∈ { 1 , 2 , … , 𝑍 } 𝑍 ∢ n u m b e r o f c o l o r s
       Graph Coloring
⎑ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎣ 𝐛 𝐞 𝐠 𝐒 𝐧 s o r t t h e s e t s a s c o n g e s t i o n d e g r e e a s { 𝑛 1 , 𝑛 2 , … , 𝑛 𝑁 } { 𝑛 1 , 𝑛 2 , … , 𝑛 𝑁 } = { 𝑣 1 , 𝑣 2 , … , 𝑣 𝑁 } ⎑ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎣ ⎑ ⎒ ⎒ ⎒ ⎒ ⎣ 𝐟 𝐨 𝐫 π‘˜ = 1 t o 𝑁 𝑖 = 1 𝐰 𝐑 𝐒 π₯ 𝐞 ( βˆƒ 𝑗 a l l o c a t e d t o c o l o r 𝑖 s t . ( 𝑗 , π‘š π‘˜ ) ∈ E S ) 𝑖 = 𝑖 + 1 𝐞 𝐧 𝐝 a l l o c a t e c o l o r 𝑖 t o π‘š π‘˜ 𝐞 𝐧 𝐝 𝐞 𝐧 𝐝