Algorithm 1.

Hierarchical FDR

1: $\mathcal{D}\leftarrow \varnothing$        Initialize discoveries

2: $\mathcal{S}\leftarrow \mathtt{\text{Root}}$                    Initialize stack

3: while $\mathcal{S}\ne \varnothing$ do

4:     choose N in $\mathcal{S}$

5:     $\mathcal{N}\leftarrow {\mathrm{\text{BH}}}_{\alpha }(\mathrm{\text{ch}}(N))$ Discoveries in children of N

6:     $\mathcal{D}\leftarrow \mathcal{D}\cup \mathcal{N}$                                        Update discoveries

7:     $\mathcal{S}\leftarrow (\mathcal{S}\backslash N)\cup (\mathcal{N}\backslash \mathcal{L})$                                    Update stack

8: end while

9: return $\mathcal{D}$ for full-tree discoveries or $\mathcal{D}\cap \mathcal{L}$ for leaves discoveries