Broadcasting Algorithms of Three-Dimensional Petersen-Torus Network

Algorithm 4

All-to-all broadcasting algorithm of 3PT(𝑙,𝑚,𝑛) under SLA model.

Step  1. Perform broadcasting among nodes located inside each module using the all-to-all broadcasting algorithm for the

Petersen graph with the SLA model in Algorithm 2.

Step  2. Every module performs the following broadcasting via internal and latitudinal edges.

(𝑧,𝑥,𝑦,1)⇛(𝑧,(𝑥+1)%𝑚,𝑦,4)⟶(𝑧,(𝑥+1)%𝑚,𝑦,0)⟶(𝑧,(𝑥+1)%𝑚,𝑦,1)⇛

(𝑧,(𝑥+2)%𝑚,𝑦,4)⟶(𝑧,(𝑥+2)%𝑚,𝑦,0)⟶(𝑧,(𝑥+2)%𝑚,𝑦,1)⇛⋯⇛

(𝑧,(𝑥−1)%𝑚,𝑦,4)⟶(𝑧,(𝑥−1)%𝑚,𝑦,2)⟶(𝑧,(𝑥−1)%𝑚,𝑦,6).

Step  3. Every module performs the following broadcasting via internal and longitudinal edges.

(𝑧,𝑥,𝑦,6)⇛(𝑧,𝑥,(𝑦+1)%𝑛,9)⟶(𝑧,𝑥,(𝑦+1)%𝑛,5)⟶(𝑧,𝑥,(𝑦+1)%𝑛,6)⇛

(𝑧,𝑥,(𝑦+2)%𝑛,9)⟶(𝑧,𝑥,(𝑦+2)%𝑛,5)⟶(𝑧,𝑥,(𝑦+2)%𝑛,6)⇛⋯⇛

(𝑧,𝑥,(𝑦−1)%𝑛,9)⟶(𝑧,𝑥,(𝑦−1)%𝑛,5).

Step  4. Every module performs the following broadcasting via internal and dimentional edges.

(𝑧,𝑥,𝑦,5)⇛((𝑧−1)%𝑙,𝑥,𝑦,0)⟶((𝑧−1)%𝑙,𝑥,𝑦,5)⇛((𝑧−2)%𝑙,𝑥,𝑦,0)⟶

((𝑧−2)%𝑙,𝑥,𝑦,5)⇛⋯⇛((𝑧+1)%𝑙,𝑥,𝑦,0).

Step  5. Perform broadcasting among nodes located inside each module using the all-to-all broadcasting algorithm for the

Petersen graph with the SLA model in Algorithm 2.