example_algorithm.tex

\begin{algorithm}[t]

  \caption{
    \label{alg:topc}
    \SYS at process $i$
  }
  
  \variables{}{
    $\candidates_i$ \tcp*{the candidates}
    $\LT_i$  \tcp*{local top-$k$}
    $\GT_i$ \tcp*{global top-$k$}
    $\delta$ \tcp*{update period}
  }

  \update{}{
    \upon{\textup{\textbf{receive}} $\langle \flagUpdate, C \rangle$ from $j$}{
      $\candidates_i[j] \leftarrow C$  \labline{topc:1} \\
      \ForEach{$(x,\any) \in C$}{ 
        $\GT_i \assign \GT_i \setminus \{(x,\any)\}$  \labline{topc:2} \\
        $\Omega \assign \sum_{(x,\omega) \in \candidates_i} \omega$  \labline{topc:3} \\
        $\GT_i \assign \GT_i \cup \{(x,\Omega)\}$  \labline{topc:4}
      }	
      $\GTi \assign \{\GTi[0], \ldots, \GTi[l-1]\}$ \labline{topc:5} \tcp*{keep top-$k$ items} 
    }
  }

  \disseminate{}{
    \textbf{let} $(\any,\Gamma) = \GT_i[k-1]$ \labline{topc:6} \tcp*{lowest score in top-$k$} 
    $l \assign k$ \labline{topc:7} \\
    \While{$l < \cardinalOf{\LT_i}$}{  \labline{topc:8}
      \textbf{let} $(x,\omega) = \LT_i[l]$ \labline{topc:9} \\
      \If{$\omega \times N \ge \Gamma$}{ \labline{topc:11} 
  	$l \assign l + 1$ \labline{topc:12} \tcp*{candidacy test passed} 
      }\Else{
  	\textbf{break}  \labline{topc:13}
      }
    }
    $C \assign \emptySet$ \labline{topc:14} %\tcp*{the top-$l$ items are candidates} 
    $n \assign 0$  \labline{topc:15} \\
    \While{ $n < l$}{ \labline{topc:16}
      $C \assign C \cup \LT_i[n]$  \labline{topc:17} \\
      $n \assign n + 1$  \labline{topc:18} \\
    }

    \ForEach{$(x,\any) \in \candidates_i$} { \labline{topc:19}
      \If{$(x,\any) \notin C \wedge (x,\omega) \in \LT_i$ }{
        $C \assign C \cup \{(x,\omega)\}$ \labline{topc:20} 
      }
      }
    

    \broadcast $\langle \flagUpdate,C \rangle$ to all sites \labline{topc:21} \\
  }

\end{algorithm}

example_listingsl.tex

\begin{figure}[!htpb]
\begin{lstlisting}[frame={tblr},numbers=none]
 every shuffling_period units do
   target = select_gossip_destination(view)
   if (target is public 
     or next_RVP(target) == target) then
     send langleRequest,view,self,targetrangle to target
   elif ((target is SYM and self is PRC) 
     or self is SYM) then
     // Use relaying
     send langleRequest,view,self,targetrangle 
       to next_RVP(target) 
   else
     // Hole punching
     send langleOpen_Hole,self,targetrangle to next_RVP(target)
     if self is not public then
       send langlePingrangle to target
   decrease_routing_table_ttls()
 
 on receive langleRequest,view_s,src,destrangle from p do
   update_next_RVP(p,p,HOLE_TIMEOUT)
   if dest != self then 
     // Forwarding 
     send langleRequest,view_s,src,destrangle to next_RVP(dest) 
   elif (src is SYM and self /*@$\neq$@*/ public) 
     or (self is SYM and src != public) then
     // Use relaying
     send langleResponse,view,srcrangle to next_RVP(src) 
   else
     send langleResponse,view,srcrangle to src
     view = merge_and_truncate(view,view_s)
     update_routing_table(view)
 
 on receive langleResponse,view_t,destrangle from p do
   update_next_RVP(p,p,HOLE_TIMEOUT)
   if dest != self then
     // Forwarding
     send langleResponse,view,destrangle to next_RVP(dest)
   else
     view = merge_and_truncate(view,view_t)
     update_routing_table(view)
  
 on receive langleOpen_Hole,src,destrangle from p do
   update_next_RVP(p,p,HOLE_TIMEOUT)
   if dest == self then
     send langlePongrangle to src
   else
     send langleOpen_Hole,src,destrangle to next_RVP(dest)
 
 on receive langlePingrangle from p do
   update_next_RVP(p,p,HOLE_TIMEOUT)
   send langlePongrangle to src
 
 on receive langlepongrangle from p do
   update_next_RVP(p,p,HOLE_TIMEOUT)
   send langleRequest,view,self,prangle to p
\end{lstlisting}
\caption{The {\nyl} protocol.}
\label{fig:nylon_code}
\end{figure}