Algorithm 1 Bridging joint $Publish$ event notifications among broker clusters.

Function: coordinateJointPublishTopic$(tp\_Id,brk\_Id,pls\_Tb,pd\_Tb,cls\_Tb)$:   1:if (! $tp\_Id$is in$pls\_Tb$ ) then   2:    addPublisher($tp\_Id$, $brk\_Id$, $pls\_Tb$);   3:    if ($tp\_Id$is in$pd\_Tb$ ) then   4:         $pd\_Scr$ = findPendingSubscribers($tp\_Id$, $pd\_Tb$);   5:         inform_to_subscribe($tp\_Id$, $pd\_Scr$);   6:    end if   7:else   8:    $cls\_Id$, $clsH\_Id$, $rlCB\_Id$ = findClusterInfo($tp\_Id$, $brk\_Id$, $pls\_Tb$, $cls\_Tb$);   9:    if ( $tp\_Id$is in$cls\_Id$’s $pls\_Tb$ ) then 10:         addPublisher($tp\_Id$, $brk\_Id$, $pls\_Tb$); 11:         $p\_Brk$ = findIntraBrokers($tp\_Id$, $cls\_Id$, $pls\_Tb$); 12:         inform_Bridging($tp\_Id$, $p\_Brk$, $p\_Brk$); 13:    else 14:         addPublisher($tp\_Id$, $brk\_Id$, $clsH\_Id$, $pls\_Tb$); 15:         $rl\_Brk$ = findInterBrokers($tp\_Id$, $pls\_Tb$, $cls\_Tb$); 16:         inform_Bridging($tp\_Id$, $brk\_Id$, $clsH\_Id$); 17:         inform_Bridging($tp\_Id$, $clsH\_Id$, $rlCB\_Id$); 18:         inform_Bridging($tp\_Id$, $rlCB\_Id$, $rl\_Brk$); 19:    end if 20:end if