Algorithm 1: Rooted Minimum Spanning Tree
input : = v[N], λ′, D = d[N][N], nr//index of root
output : Pre [N]/*The index of the parent node of v[n], equivalent to ℰ	*/
begin
/*For simplicity, set ri = 1 in (8)	*/
/*Vertex in tree	*/
= {v[nr]};
for v[n] ∈ – do
/*distance from the tree	*/
dtree[n] = d[nr] [n];
/*distance from the root	*/
droot [n] = $\frac{1}{{\lambda }^{\prime }}$ d[nr] [n];
Pre[n] = nr;
while ≠ do
m = minv[n]∈ – droot[n];
= ∪ v[m];
droot [m] = droot[Pre[m]] + $\frac{1}{{\lambda }^{\prime }}$ dtree [m];
for v[n] ∈ – do
if droot[n] > d[m] [n] + droot[m] then
dtree [n] = d[m] [n];
droot [n] = d[m][n] + droot[m];
Pre[n] = m;
end