# Lightweight Path Recovery in IPv6 Internet-of-Things Systems
## 5 Performance Evaluation and Analysis
### Performance Improvement Analysis  
Our proposed LiPa algorithm has two features compared to other existing works: On the one hand, it adds the information of grandparent nodes in addition to that of parent nodes. On the other hand, it utilizes the information of multiple collection cycles instead of the present cycle only. Therefore, we specifically analyze the effect of these two features on the performance improvement of the LiPa algorithm separately. To this end, two variation of LiPa are introduced:  
**LiPa-S** mainly leverages the spatial information of the parent and grandparent nodes but sets \(\tau=0\), i.e., the LiPa algorithm with a sliding window size of 1. Without the temporal information of multiple collection cycles, this variation is introduced to verify the effectiveness of the adaptive sliding window of LiPa.  
**LiPa-T** mainly uses the temporal information of the sliding window size of \(\tau=[\frac{1}{Ratio_{active}}]\) but only records the information of the parent node, i.e., the LiPa algorithm with only two path relevance cases, case 2 and case 4, mentioned in Section 4. Without sufficient spatial information, we can observe the performance improvement of LiPa by appending the grandpa node's information, thus adding the other four possible path correlations cases mentioned in Section 4.  
Figure 6 shows the accuracy of LiPa-S, LiPa-T, and LiPa in different network scenarios. As shown in Figure 6a, when the number of nodes is 300, and the percentage of fault nodes is 5%, the accuracy of the 3 LiPa algorithms improves as the active ratio of nodes changes, and LiPa's accuracy is consistently higher than LiPa-S and LiPa-T. The accuracy improvement of the LiPa algorithm over LiPa-S is 33% on average and up to 78%. The accuracy improvement of the LiPa algorithm over LiPa-T reaches an average of 19% and 34% at the most. As shown in Figure 6b, when the percentage of fault nodes is 5%, and the active ratio of nodes is 30%, the accuracy of the 3 LiPa algorithms decreases as the number of nodes changes, but the accuracy of LiPa is still consistently higher than that of LiPa-S and LiPa-T. The accuracy improvement of the LiPa algorithm over LiPa-S reaches an average of 55% and a maximum of 62%. The accuracy improvement of the LiPa algorithm over LiPa-T reaches an average of 19% and 25% at most. As shown in Figure 6c, when the number of nodes is 300, and the active ratio of nodes is 30%, the accuracy of the 3 LiPa algorithms decreases as the percentage of fault nodes changes, but the accuracy of LiPa is still consistently higher than that of the LiPa algorithm over LiPa-S is 59% on average. The accuracy improvement of the LiPa algorithm over LiPa-T is the highest, reaching an average of 26%. These results are because both LiPa-S and LiPa-T are neutered versions of LiPa, drawing only one of the two features of LiPa.  
We can conclude that: (1) From the difference between LiPa and LiPa-S, our practice of setting an observation window can improve the performance by about 50% on average. (2) From the gap between LiPa and LiPa-T, our practice of appending grandparent nodes can improve the performance by about 20% on average. (3) In combination, the performance improvement from setting observation windows is more significant than appending grandparent nodes.