Algorithm 1 Pseudo-code of Randomized Prim

Require:$G=(V,E)$ and adjacency matrix $D=d_{ij}$   for all edges $i.j$; 1:Choose any vertex $i\in V$ 2:$T\stackrel{}{\leftarrow }\left\{i\right\}$; 3:$M\stackrel{}{\leftarrow }V\backslash \left\{i\right\}$; 4:$T_{min}\stackrel{}{\leftarrow }\varnothing$; 5:while$\mid T\mid \ne \mid V\mid$do 6:   Find an edge $(j,k)\in E$ such that $j\in T,k\in M$    and $d_{jk}$ is minimum; 7:   $T\stackrel{}{\leftarrow }T\cup \left\{k\right\}$; 8:   $M\stackrel{}{\leftarrow }M\backslash \left\{k\right\}$; 9:   $T_{min}\stackrel{}{\leftarrow }{T}_{min}\cup$ (j,k); 10:end while 11:return$T_{min}$;