## 2 Related Works  
In the present subsection, we describe the works on differential privacy for sequential pattern mining. Most of them add Laplace noise to the prefix tree while building the sequential patterns [8; 9; 10; 11]. [PERSON] et al. [12] applied differential privacy to publish prefix trees for transit data by adding Laplace noise to the prefix tree count at each \(h\) level. Afterward, they calculated the frequent patterns using the _PrefixSpan_ algorithm on the sanitized data and measured the utility as the true and false positives for the top-\(k\) frequent sequences. They performed their experiments on data from Canada's metro and bus networks. Similarly, in [8], differential privacy was added to n-grams. They experimentally evaluated their solution in terms of the data analysis tasks of count query and frequent sequential pattern mining, with data from the page views of msnbc.com (i.e., MSNBC) and from the sequences of stations visited by passengers in the Montreal transportation system (i.e., STM). [PERSON] and [PERSON] [13; 14] applied a two-phase algorithm for differential privacy in sequential pattern mining. The first phase adds Laplace noise to release a differentially private prefix tree \(T^{\prime}\). The second phase constructs a dataset sketch and refines the candidate patterns count, finally using the remaining \(\varepsilon\)-budget to retrieve the final counts, obtaining the top-\(k\) most frequent patterns. Their utility measure was the \(F_{1}\)-score. [PERSON] et al. [9; 10] observed that in differentially private frequent sequence mining (FSM), the amount of required noise is proportionate to the number of candidate sequences, and they proposed the \(\textit{PFS}^{2}\) privacy-aware algorithm to extract frequent patterns. To improve the utility and privacy trade-off, they leveraged a sampling-based candidate pruning technique. Then, they performed the experimental evaluation on the MSNBC, House Power, and Bible datasets to compare \(\textit{PFS}^{2}\) with the Prefix [12] and \(n\)-gram [8] algorithms, in terms of the F-score and relative error measures. [PERSON] and [PERSON] [11] proposed to truncate frequent patterns to add noise to the pattern support based on the geometric mechanism to satisfy \(\varepsilon\)-differential privacy. Differential Private Frequent Sequence Mining (DP-FSM) aims to generate all candidate sequences and add noise to each candidate sequence's support. Later on, the algorithm selects frequent sequences according to the amount of noise added to the candidate. The noise depends on the sensitivity that should be reduced for accurately estimating which candidate sequences are frequent. The sensitivity depends on the size of the sequence candidate. The authors showed that their approach outperformed the \(\textit{PFS}^{2}\) algorithm [10] in terms of the _false negative rate_ and _relative support error_. [PERSON] et al. [15] suggested a framework to minimize privacy leaks from medical distributed records. The first step is to extract frequent patterns from each data source. Thus, the authors applied differential privacy over the support count of the extracted patterns. Then, the frequent patterns from all local data sources were aggregated in the case and control lists. Oncethe lists were aggregated in a centralized location, they computed the union of patterns and carried out the summation of the support counts of each pattern. Finally, based on the aggregated list of patterns, the top-\(k\) patterns were chosen to be used as the feature representation.