Algorithm 1: The KMST tree-filtering algorithm, TF_KMST

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

Output: top-k RSTs.

1: $Q\leftarrow ⌀;\rho \leftarrow 0;T\leftarrow Prim\left(G\right)$ 2: while $W\left(T\right)<\omega$ do 3:    $T\leftarrow GenNext\left(\right)$ 4:    $\rho \leftarrow Q.min\left(\right).probability\left(\right)$ 5:    if $Q.size\left(\right)<k$ then 6:        $Q.insert\left(T\right)$ 7:    else if $P\left(T\right)>\rho$ then 8:         $Q.remove\_min\left(\right)$;$Q.insert\left(T\right)$ 9:    end if 10: end while 11: return $Q.all\left(\right)$