Algorithm 1. Tree growing.
Input:$G=(V,E)$, traveling distance constraint $L$;
Output: spanning tree $T$
1:	$T:=\left\{v_0\right\}$
2:	while$C(T)\le L$ and $V\backslash T\ne \varphi$ do
3:		$R:=\varphi$
4:		for each $v_i\in V$ and $v_i\notin T$ do
5:			$c_i:=\underset{v_k\in T}{\min }{c}_{ik}$
6:			$c_i^{\prime }:=\min \{c_i,c_i+c_{p(k)i}-c_{p(k)k}\}$
7:			$R(i,T):={\widehat{r}}_i/c_i^{\prime }$
8:			$R:=R\cup \{R(i,T)\}$
9:		end for
10:		find the biggest $R(i,T)$ in $R$
11:		$v_i:=\arg \underset{R(i,T)\in R}{\max }R(i,T)$
12:		$C(T\cup \{v_i\}):=2(c_{p(i)i}+{\displaystyle {\sum }_{\begin{array}{l}{v}_k\in T,\\ k\ne 0\end{array}}{c}_{p(k)k}})$
13:		if $C(T\cup \{v_i\})\le L$ then
14:			$C(T):=C(T\cup \{v_i\})$
15:			$T:=T\cup \left\{v_i\right\}$
16:		else
17:			break
18:		end if
19:	end while
20:	return$T$