Algorithm 3 PFS2 Algorithm
Input:
	Original database D; Threshold θ; Maximal length constraint upper bound l1;
	Percentage η; Privacy budgets ε1, …, ε5.
Output:
	Frequent Sequences FS;
1:	/**** Pre-Mining Phase ****/
2:	|D| ← get the noisy number of total input sequences using ε1;
3:	for l2 = 1; p < η; l2 ++ do
4:	αl2 = get the noisy number of input sequences with length l2 using ε2;
5:	$p=({\sum }_{j=1}^{l_2}{\alpha }_j)/|D|$;
6:	end for
7:	lmax ← min{l1, l2};
8:	β ← get noisy maximal support of sequences of length from 1 to lmax using ε3;
9:	Lf ← estimate_max_frequent_sequence_length (θ, β);
10:	/**** Mining Phase ****/
11:	FS ← ø;
12:	dbSet ← randomly_partition_database (D, Lf);
13:	ε′ ← ε5/Lf;
14:	for k from 1 to Lf do
15:	if k == 1 then
16:	Candidate Set Ck ← all items in the alphabet;
17:	else
18:	Candidate Set Ck ← generate_candidates (FSk—1);
19:	end if
20:	$C_k^{\prime }$ ← Sampling_based_Candidate_Pruning(Ck, dbk, ε4, θ, lmax); /**** See Algorithm 1 ****/
21:	FSk ← discover_frequent_sequences ( $C_k^{\prime }$, D, ε′, θ);
22:	FS += FSk;
23:	end for
24:	return FS;