Algorithm 2. The spanning tree algorithm

1. Input: an OCRG; 2. Output: a spanning tree with the mobile sink as the root node; 3. Add $v_{\sin k}$ into set K; 4. Add the remaining nodes in the OCRG into set U; 5. for each node $v_i$ in set U do //  initialization 6. if ($v_i$ is directly connected to $v_{\sin k}$) 7. ${PC}_{path(v_{\sin k},v_i,\ast )}$ = $P_{v_{\sin k}{v}_i}$;   //${PC}_{path(v_{\sin k},v_i,\ast )}$ is the PC of the path from $v_{\sin k}$ to $v_i$ 8. $PATH(v_{\sin k},v_i,\ast )$ = {$v_{\sin k}$,$v_i$}; //$PATH(v_{\sin k},v_i,\ast )$ is used to store the nodes on the path from $v_{\sin k}$ to $v_i$ 9.  else 10. ${PC}_{path(v_{\sin k},v_i,\ast )}$ = 0; 11. $PATH(v_{\sin k},v_i,\ast )$ = ∅; 12.  end if 13.  end for 14. ${PC}_{path(v_{\sin k},v_{\sin k},\ast )}$ = 1;    // set the PC of the path from $v_{\sin k}$ to $v_{\sin k}$ is 1 15. while (set U is not empty) 16. Select the node $v_i$ with max ${PC}_{path(v_{\sin k},v_i,\ast )}$ from set U; 17. Transfer $v_i$ from set U to set K; 18. for each neighbor $v_j$ of $v_i$ do    //$v_j$ is still in set U 19. temp ←${PC}_{path(v_{\sin k},v_i,\ast )}$×$P_{v_i{v}_j}$; 20. if (temp > ${PC}_{path(v_{\sin k},v_j,\ast )}$) 21. ${PC}_{path(v_{\sin k},v_j,\ast )}$← temp;  // update the PC of the path from $v_{\sin k}$ to $v_j$ 22. $PATH(v_{\sin k},v_j,\ast )$←$PATH(v_{\sin k},v_i,\ast )$ + $v_j$; // update the nodes on the path from $v_{\sin k}$ to $v_j$ 23.  end if 24.  end for 25.  end while