Algorithm 2: The DFS based tree-filtering algorithm, TF_DFS

Input: An uncertain graph G, an integer k, a weight threshold $\omega$.

Output: top-k RSTs.

1: $Q\leftarrow ⌀;\rho \leftarrow 0;T\leftarrow \left\{V_r\right\}$ 2: while $T\leftarrow SD\_DFS\_GROW\left(T\right)$ do 3:    $\rho \leftarrow Q.min\left(\right).probability\left(\right)$ 4:    if $W\left(T\right)>\omega$ then 5:        $prune\_rule1\left(\right)$ 6:    else if $Q.size\left(\right)$==k and T is not a spanning tree and $P\left(T\right)<\rho$ then 7:        $prune\_rule2\left(\right)$ 8:    else if $Q.size\left(\right)<k$ and T is a spanning tree then 9:        $Q.insert\left(T\right)$ 10:    else if $P\left(T\right)>\rho$ and $Q.size\left(\right)$==k then 11:        $Q.remove\_min\left(\right)$;$Q.insert\left(T\right)$ 12:    end if 13: end while 14: return $Q.all\left(\right)$