Algorithm 2. Determination of the minimum communication radius of inters cluster communication.

Input: the sensor node set $S=\{s_1,s_2,\cdots ,s_N\}$, the number of cluster head k.

Output: the set of relay nodes RS.

1. Suppose all nodes in the set $S$ as generic point, generates the corresponding k order Voronoi diagram $V_k(S)$;

2. The set of polygon for Voronoi diagram is denoted as $V=\{V_k(P{L}_1,S),$ $V_k(P{L}_2,S),$ $\cdots ,V_k(P{L}_M,S)\}$, where $V_k(P{L}_1,S)$ is the i-th polygon for $V_k(S)$;

3. $RS=\varnothing$;

4. while $V\ne \varnothing$ do

5.    for each $V_k(P{L}_i,S)\in V$ do

6.      if $s_j$ is the generic point of polygon $V_k(P{L}_i,S)$ then

7.        record the occurrence time of node $s_j$;

8.      end if;

9.   end for;

10. Find out the $s_{\max }$ which denotes the maximum number of occurrences of generic point;

11. The node $s_{\max }$ can be added in the set of $RS$;

12. $V=V-\{V_k(P{L}_i,S)|s_{\max }\in P{L}_i\}$;

13. end while.