# An Efficient Dummy-Based Location Privacy-Preserving Scheme for Internet of Things Services
## 4 Experimental Results and Analysis
With an increase in \(k\), the run time of the DLP scheme increases rapidly but the Enhanced-DLP run time varies little. And the run time of the Enhanced-DLP is 68.14% lower than that of the DLP. The reason is that the DLP scheme adopts the greedy scheme to select \(k-1\) dummy locations, which needs to calculate all the residual locations in candidate set to ensure the current set has the largest entropy. While the Enhanced-DLP scheme adopts the enhanced greedy manner, which only needs to calculate \(p_{max-min}\) and \(p_{min-max}\) to successively select \(k-1\) dummy locations to ensure the largest entropy. Furthermore, the computational complexity of the DLP scheme (i.e., O(\(n^{2}\))) is higher than the Enhanced-DLP scheme (i.e., O(\(n\))), where \(n\) and \(k\) are the same. The experimental results \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & \multicolumn{4}{c}{**Anonymity Degree: k**} \\ \cline{2-5}  & **k = 15** & **k = 20** & **k = 25** & **k = 29** \\ \hline DLP & 0.019 s & 0.117 s & 0.217 & 0.298 s \\ DLS & 0.431 s & 3.184 s & 6.870 s & 10.553 s \\ CircleDummy & 1.236 s & 9.003 s & 19.316 s & 29.604 s \\ GridDummy & 0.00003 s & 0.0002 s & 0.0004 s & 0.0006 s \\ Enhanced-DLP & **0.018 s** & **0.116 s** & **0.215 s** & **0.295 s** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Run times for Scenario 1. Figure 3: Scenario 1: Entropy and run time. are also consistent with the results of our analysis. The run time of Enhanced-DLP is much lower than that of DLP. Figure 5 illustrates the probability of query recognition under an ADLS attack for three different scheme. As the value of k increases, the probability of query recognition of three schemes is gradually reduced, which indicates that it is more difficult to get the user's real location from the anonymous set. The DLS scheme has the highest probability of query recognition under the same attack. The reason is that once the history query probabilities of two locations are different in the DLS scheme, their chosen optimal dummy location sets must be different. In this property, an adversary can easily identify the user's real location from an anonymous set. We can also see that the probability of query recognition of the Enhanced-DLP and the DLP scheme is the lowest. Although the query recognition probability of the DLP scheme decreases with the increase of \(k\), the probability of query recognition is still higher than that of the Enhanced-DLP scheme. Moreover, the probability of query recognition of the Enhanced-DLP is 33.63% lower than that of the DLP scheme. The probability of query recognition of the Enhanced-DLP scheme does not vary much with the increase of anonymity degree \(k\). This is because the Enhanced-DLP scheme adopts an enhanced greedy scheme to successfully select dummy locations which ensures the entropy of the current anonymous set is the largest, while the DLP scheme adopts the greedy scheme to select dummy locations using the enumeration scheme from the candidate set. This is vulnerable to privacy breaches from ADLS attacks and requires more time to generate anonymous sets. Figure 5: Scenario 2: The probability of query recognition versus \(k\). Figure 4: Scenario 2: Entropy and run time.