An Efficient Algorithm to Find Broadcast Schedule in Ad Hoc TDMA Networks

Algorithm 1

Outline of broadcast scheduling algorithm.

Input:   FSM table of network

Output:   ${\Re }_m$ - Optimum cover

(1) From FSM table of network, generate all compatible (incompatible) pairs;

     If (no compatibles)  $\{$

        ${\Re }_m$   ← set of states $\epsilon ;$

       stop;  $\}$

     else Find maximal compatibles ${\mathrm{\Omega }}_m$ and incompatibles ${\mathrm{\Omega }}_i;$

(2) Find the tight lower bound L and the bound incompatible ${\text{IC}}_b;$

(3) Form compatible groups CG with respect to ${\text{IC}}_b;$

(4) Let limit = min $(|{\text{CG}}_1|,100);$   $j=1;$  Let $s_1$be the first state in ${\text{IC}}_b;$

(5)  while (j$<$ limit) $\{$

    Include in schedule $\Re (j),$ compatible ${\text{C}}_j\in \text{CG(}{s}_1\text{)};$

     for (every state $s_i\in {\text{IC}}_b$ where $s_i$ ≠ $s_1$) $\{$

      (a) Apply selection criteria and include a compatible ${\text{C}}_n\in \text{CG(}{s}_i\text{)}$ in $\Re (j);$

      (b)  for (every state $s_k\in {\text{C}}_n$)  Increment utility factor $\mu (s_k);$   $\}$

     for (every state $s_i\mid s_i\in \epsilon ,s_i\notin \Re (j)$)

      Include in $\Re$(j) largest cardinality compatible covering the state $s_i;$

     $j=j+1;$   $\}$

(6)  for (every $\Re$(j))

    compute the performance indices and choose ${\Re }_m.$