Adaptive Broadcasting Mechanism for Bandwidth Allocation in Mobile Services

Algorithm 1

Broadcast-Tree Construction Procedure:

(0) Initial settings: Let h = 0, m = N, 𝐿=∑^𝑁_𝑖=1𝑆(𝐷_𝑖), and 𝑛_𝑖=1 for 𝑖=1,2,…,𝑁

(1) Let  𝐹(𝑟)=(𝐿/2^ℎ+2)∑^𝑟_𝑖=1Pr𝐷_𝑖−∑^𝑟_𝑖=1(Pr(𝐷_𝑖)/4)+2^ℎ−1∑^𝑁_𝑖=𝑟+1(Pr(𝐷_𝑖)/𝑛_𝑖)∑^𝑟_𝑖=1𝑆𝐷_𝑖.

  Find the cutpoint  𝑐 such that 𝐹(𝑐)=max_{1≤𝑟≤𝑚}{𝐹(𝑟)}.

(2) If  𝐹(𝑐)≤0 or  ℎ>𝜏, then return the expanded full binary tree ℑ.

(3) else  move the data items {𝐷₁,…,𝐷_𝑐} to the next level.

(4) Set  ℎ=ℎ+1, 𝑚=𝑐, 𝐿=𝐿+∑^𝑐_𝑖=1𝑛_𝑖𝑆(𝐷_𝑖), and 𝑛_𝑖=2^ℎ for 𝑖=1,2,…,𝑐. Then go to step (1).