## 6 Experiments
### Cache  
Although the entropy approach significantly reduced execution times, some values still need to be improved for practical use. The **Cache** strategy can ensure the feasibility of executing risk assessments efficiently. By leveraging the **Cache** strategy, we can substantially reduce execution times, making the process more practical and manageable. This method ensures that risk assessments can be conducted within reasonable time frames, thereby enhancing the overall efficiency and effectiveness of the evaluation process.  
Table 13 compares execution times for various attacks on location and time features using the **Original** and **Cache** approaches across three different datasets: Wi-Fi, Foursquare, and Breadcrumbs. For location visit attacks (\(k=1\)), the **Original** approach's execution times are significantly longer than those of the **Cache** approach, with reductions from 2314 days to 12 h in the Wi-Fi dataset, from 6 days to 2 min in the Foursquare dataset, and from 7 days to 2 min in the Breadcrumbs dataset. For visit attacks (\(k=2\)), similar  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Feature** & **Attack** & **k** & \multicolumn{6}{c}{**Low-Entropy Percentile (\%)**} \\  & & & & **Original** & **10** & **20** & **30** & **40** & **50** \\ \hline
**Location** & Visit & 1 & 6 0 d0:47:08 & 0 d 15:43:13 & 1 d 07:29:38 & 1 d 23:06:18 & 2 d 15:22:10 & 3 d 07:28:55 \\
**Location** & Visit & 2 & 512,40 d 00:00:00 & 10:09:40 & 0:05:37 * & 19,269 d 10:44:57 * & 27,007 d 01:13:54 * & 38,389 d 02:03:27 * & 39,641 d 04:36:2* \\
**Time** & Visit & 1 & 5 d 12:13:19 & 0 d 13:04:29 & 1 d 25:054 & 1 d 16:05:08 & 2 d 03:07:10 & 2 d 16:20:52 \\
**Time** & Visit & 2 & 27,423 d 16:06:48 * & 7681 d 2:45:46 * & 13,257 d 00:33:28 * & 20,222 d 18:00:00 * & 26,018 d 14:16:43 * & 30,54 d 182:45* \\
**Location** & Location Sequence & 1 & 1 d 13:07:10 & 0 d 03:53:55 & 0 d 07:41:12 & 0 d 113:045 & 0 & 1 e 152:94:44 & 0 d 19:26:50 \\
**Location** & Location Sequence & 2 & 30,023 d 22:56:36* & 5898 d 14:19:11* & 11,089 d 04:50:01 * & 15,697 d 02:44:33* & 19,623 d 12:54:34* & 23,099 d 20:03:44 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Foursquare dataset: comparing execution time of the **Original** with the **Low-Entropy Percentile** approach.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Feature** & **Attack** & **k** & \multicolumn{6}{c}{**Low-Entropy Percentile (\%)**} \\  & & & **Break** & **10** & **20** & **30** & **40** & **50** \\ \hline
**Location** & Visit & 1 & 0 d 03:51:48 & 0 d 01:10:00 & 0 d 01:28:13 & 0 d 01:43:45 & 0 d 01:57:22 & 0 d 02:08:09 \\
**Location** & Visit & 2 & 12 d 08:03:21 & 3 d 18:13:14 & 3 d 18:40:56 & 3 d 18:58:12 & 3 d 19:04:23 & 3 d 19:07:03 \\
**Time** & Visit & 1 & 0 d 09:14:02 & 0 d 00:58:20 & 0 d 00:59:45 & 0 d 01:00:36 & 0 d 01:01:26 & 0 d 01:01:55 \\
**Time** & Visit & 2 & 25 d 03:46:50 & 2 d 22:27:40 & 2 d 22:48:25 & 2 d 23:07:16 & 2 d 23:16:15 & 2 d 23:19:30 \\
**Location** & Location Sequence & 1 & 0 d 01:29:24 & 0 d 00:18:53 & 0 d 00:39:13 & 0 d 00:47:09 & 0 d 00:55:15 & 0 d 01:03:27 \\
**Location** & Location Sequence & 2 & 7 d 07:37:38 & 2 d 06:03:07 & 2 d 06:29:51 & 2 d 06:54:20 & 2 d 07:03:17 & 2 d 07:08:42 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Foursquare dataset: Comparing execution time of **Break** with **Break** and **Low-Entropy Percentile**.  
reductions are observed, with **Original** times decreasing from 60,395 days to 11 days (Wi-Fi), 51,240 days to 3 min (Foursquare), and 69 days to 9 min (Breadcrumbs). For time visit attacks (\(k=1\) and \(k=2\)), the **Cache** approach consistently reduces execution times from thousands of days to a few days or minutes across all datasets. Location sequence attacks also show substantial reductions, with **Cache** times significantly shorter than **Original** times across all datasets. The **Cache** approach effectively reduces execution times for all attack types and datasets.