Algorithm 1 A broadcast slot (BS) scheduling algorithm

//N = the number of BSs to be scheduled

//m = the number of children

//BSN(i) = the BS number assigned to node i

If i is a sink then

$\mathrm{S}\left(\mathrm{i}\right)=\left\{\left(i_j,B{S}_k\right)|k=\left(j-1\right) mod N+1, 1\le j\le ⎣\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$2$}\right.⎦\right\}$ $\cup$

$\left\{\left(i_j,B{S}_k\right)| k=\left(j-\left(⎣\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$2$}\right.⎦+1\right)+⎣\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$2$}\right.⎦\right) mod N+1,⎣\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$2$}\right.⎦<j\le m\right\}$

If i is an intermediate node then

$\mathrm{S}\left(\mathrm{i}\right)=\left\{\left(i_j,B{S}_k\right)| k=\left(BSN\left(i\right)+j-2\right) mod N+1, 1\le j\le m\right\}$