Algorithm 1 Communication Planning Algorithm
Require:${[X_0,{\Sigma }_0,M,P]}^r,\forall r\in \mathcal{R},T,{\sigma }_{max}$
Ensure:$\pi$	▹ Robot Communication Policy
1: ▹ Particle filter for each robot
2: $Q_0.sims\leftarrow$PF($([X_0,{\Sigma }_0,M,P]$)${}^r,\forall r\in \mathcal{R}$	▹ Queue
3: $Q_0.parent\leftarrow 0$
4: $G.node{s}_0\leftarrow 0$	▹ Cost Graph
5: $m=0$
6: for $t=1$ to T do
7:    $\mathcal{P}=Q.parent$	▹ List of current leaf nodes
8:    ▹ Update $Q_i$ without communication a
9:    for $i=\left|Q\right|$ to 1 do
10:        $\eta \leftarrow PF\_Update(Q_i,a=false)$
11:        if $\eta .\sigma <Q_0.\sigma \times {\sigma }_{max}$ then
12:           $m=m+1$
13:           $p=Q_i.parent$
14:           $Q_{i+1}.sims\leftarrow \eta$
15:           $Q_{i+1}.parent\leftarrow m$
16:           $G.node{s}_m\leftarrow \eta .\sigma$
17:           $G.edge{s}_{p,m}\leftarrow 0$
18:    ▹ Update $Q_i$ with communication
19:    $m=m+1$
20:    $Q_0.sim\leftarrow$PF_Update($N_{0,t-1},a=true$)${}^r,\forall r\in \mathcal{R}$
21:    $Q_0.parent\leftarrow m$
22:    $G.node{s}_m\leftarrow Q_0.\sigma$
23:    $G.edge{s}_{\mathcal{P},m}\leftarrow 1$
24: $\pi \leftarrow$LowestCostPath(G)	▹ Search over Graph