Algorithm 2 Maximum-Weighted Clique Beam Scheduling Algorithm.

Require: $\mathcal{G}=(\mathcal{V},\mathcal{E})$, $\mathcal{W}=\{w_1,w_2,\dots ,w_N\}$. Ensure: ${\mathcal{Q}}_m$. 1:Initialize: 2:Let ${\mathcal{Q}}_k$ = Ø, $k\in \{1,2,\dots ,K-1\}$; 3:Let ${\mathcal{Q}}_K=\left\{v_K\right\}$; 4:Let $W_{{\mathcal{Q}}_k}=0,k\in \{1,2,\dots ,K-1\}$; 5:Let $W_{{\mathcal{Q}}_K}=w_K$; 6:Let ${\mathcal{Q}}_m={\mathcal{Q}}_K$; 7:Let $max=W_{{\mathcal{Q}}_K}$ 8:Let ${\mathcal{S}}_k=\{v_k,v_{k+1},\dots ,v_K\},k\in \{1,2,\dots ,K\}$; 9:Scheduling: 10:for$k=K-1:1$do 11:   if $\left\{v_k\right\}\cup {\mathcal{Q}}_{k+1}$ is also a clique then 12:     ${\mathcal{Q}}_k={\mathcal{Q}}_{k+1}\cup \left\{v_k\right\}$; 13:     $W_{{\mathcal{Q}}_k}=W_{{\mathcal{Q}}_{k+1}}+w_k$; 14:   else 15:     ${\mathcal{Q}}_k=\left\{v_k\right\}$; 16:     $W_{{\mathcal{Q}}_k}=w_k$; 17:     ${\mathcal{S}}_k={\mathcal{S}}_k\cap \mathcal{N}\left(v_k\right)$ 18:     if ${\mathcal{S}}_k$ = then 19:        if $W_{{\mathcal{Q}}_k}>max$ then 20:          ${\mathcal{Q}}_m={\mathcal{Q}}_k$; 21:          $max=W_{{\mathcal{Q}}_k}$; 22:          $mc=k$; 23:        end if 24:        return; 25:     end if 26:     while ${\mathcal{S}}_k\ne$ do 27:        $j=min\left\{j\right|v_j\in {\mathcal{S}}_k\}$; 28:        ${\mathcal{Q}}_k={\mathcal{Q}}_k\cup \left\{v_j\right\}$; 29:        $W_{{\mathcal{Q}}_k}=W_{{\mathcal{Q}}_k}+w_j$; 30:        ${\mathcal{S}}_k=({\mathcal{S}}_k-\left\{v_j\right\})\cap \mathcal{K}\left(v_j\right)$; 31:        if ${\mathcal{S}}_k=$ then 32:          if $W_{{\mathcal{Q}}_k}>max$ then 33:             ${\mathcal{Q}}_m={\mathcal{Q}}_k$; 34:             $max=W_{{\mathcal{Q}}_k}$; 35:             $mc=k$; 36:          end if 37:        end if 38:     end while 39:     if $mc\ne k$ then 40:        ${\mathcal{Q}}_k={\mathcal{Q}}_{k+1}$; 41:        $W_{{\mathcal{Q}}_k}=W_{{\mathcal{Q}}_{k+1}}$; 42:     end if 43:   end if 44:end for 45:if$|{\mathcal{Q}}_m|>J$ then 46:   ${\mathcal{Q}}_m={\mathcal{Q}}_m(1:J)$; 47:else 48:   return; 49:end if