Algorithm 1: The ABRCD scheme

Input: A set of nodes, $\mathcal{M}\triangleq \left\{v=v_0,v_1,v_2, \dots ,v_m\right\}$, with their coordinates. And AT(v), ∀v∊$\mathcal{M}$ 1.   for each node $v_i$ from $v_1$ to $v_m$ do 2.        Calculate $d_{v_i}$ using its coordinates 3.        Calculate $n_{v_i}$ using Equation (11) 4.        Calculate $r_{v_i}$ using Equation (12) 5.   end for 6.   Construct graph G = ($\mathcal{M},$ ℰ) based on coordinates and radius of each node 7.   Conduct BFS on G starting from $v_0$, obtain the level of each node $\mathrm{L}$(v), and take the order of BFS as id for each node 8.   Find the Minimum Covering Node Sets ${\mathrm{C}}_i$, i∊T 9.   Build Covering Sub-tree, and obtain the set of root and parent of each node, Root and Pr 10.   Finalize Backbone: //Backbone is denoted as B 11.   for l in [max({L(x)}) .. 1] do 12.        for each node v, L(v) = l do 13.             if L(Root(CovNode(v))) < L(v) then      //Case 1 14.                  Pr(v) ← CovNode(v) 15.             else 16.                  Find a forwarderu, satisfying       //Case 2 17.                  (1) v$\in$N(u) 18.                  (2) [u$\in$B and L(Root(u)) < L(v)] or [L(Root(CovNode(u))) < L(v)] 19.                  if such a forwarder u exists then 20.                       Pr(v) ← u 21.                       AddToBackbone(u, CovNode(u), AT(v)) 22.                  else //Case 3 23.                       Find two forwarders u and f, satisfying 24.                       (1) v$\in$N(u) and u$\in$N(f) 25.                       (2) [f$\in$B and L(Root(f)) < L(v)] or [L(Root(CovNode(f))) < L(v)] 26.                       Pr(v) ← u 27.                       Pr(u) ← f 28.                       AddToBackbone (f, CovNode(f), AT(u)) 29.                       AddToBackbone (u, f, AT(v)) 30.                  end if 31.             end if 32.             Root(v) ← Root(Pr(v)) 33.        end for 34.   end for 35.   procedureAddToBackbone(x, p, t) 36.   if x∊B then 37.        B ← B∪{x} 38.        Pr(x) ← p 39.        Root(x) ← Root(p) 40.   end if 41.   ST(x) ← ST(x)∪{t} 42.   end procedure Output: B, ST and Pr