Algorithm 3.

Conditional Exponential Method

Input:
	Candidate i-subgraphs Ci; Privacy budget ϵc; Threshold θ; The number of frequent i-subgraphs ni;
Output:
	Frequent i-subgraphs Fi;
1:	ϵc1 ← βϵc, ϵc2 ← (1-β)ϵc;
2:	for j from 1 to ni do
3:	Ci’ ← ∅;
4:	for each subgraph g in Ci do
5:	$n{s}_g=s_g+Lap(\frac{2n_i}{{ϵ}_{c1}})$;
6:	if nsg ≥ θ then
7:	add g into Ci’;
8:	end if
9:	end for
10:	if Ci’ is not empty then
11:	gj ← select a subgraph from Ci’ such that $\text{Pr}[\text{Selecting}\text{subgraph}g]\propto \text{exp}(\frac{{ϵ}_{c2}\times s_g}{2n_i})$;
12:	remove gj from Ci;
13:	add gj into Fi;
14:	end if
15:	end for
16:	return Fi;