**6. Conclusions**

In this paper, we proposed an improved equal-cost multi-path shortest path algorithm (ECMP-Dijkstra) and accordingly proposed three SDN interception models T model, ECMP-T model, and Fermat-point model, to deploy the best intercept access point reasonably in three real-world hybrid SDN topologies. Subsequently, we proposed a restrictive minimum

vertex coverage algorithm (RMVCA) to intercept the whole interception system with the least SDN nodes, and to optimize the deployment efficiency of intercept access points and improve the intercept link coverage, so as to optimize the performance of the whole intercepting system. According to RMVCA, we analyze the effect of different SDN node ratios on the intercept link coverage and the minimum vertex coverage set. Considering the intercept link coverage and the minimum vertex coverage set, we found a suitable SDN node ratio for deploying intercept access points reasonably, namely, to intercept the whole hybrid SDN with the least SDN nodes.

Based RMVCA, we put forward three approaches PA, RA, and HA for experiments, and compared the three experimental approaches. The experimental results show that HA is the best approach, which can significantly optimize the efficiency of deploying intercept access points (i.e., optimize TTC) and improve the intercept link coverage of the whole hybrid SDN.

By the way, we analyzed the influence of three SDN interception models on various performance metrics of lawful interception system using three real-world topologies. The simulation results reveal that the three SDN interception models have little effect on the intercept link coverage, and T model and ECMP-T model have no effect on user's traffic transmission quality. Compared with T model and ECMP-T model, Fermat-point model is the best interception model for the reason that Fermat-point model can make MILC, TOC, NFD the lowest by sacrificing a small part of user's traffic transmission quality (UQoS) and deployment time (TTC), intercepting the whole hybrid SDN at dramatically lower costs.

This paper has not considered the traffic bottleneck (link capacity) problem but has proposed the deployment and optimization strategy of intercept access points that pave the way for the future work that joint deployment of IAPs and LEAs in H-SDNs based on the consideration of the traffic bottleneck problem.

**Author Contributions:** X.X. and W.-K.J. conceived and designed the study. X.X. performed the simulations. X.X. wrote the paper. Y.W. and X.W. reviewed and edited the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was financially supported by the National Natural Science Foundation of China No. U1805262, No. 61871131, and No. 61701118 in part by the Natural Science Foundation of Fujian Province, China No.2018J05101, 2018H6007, and Special Fund for Marine Economic Development of Fujian Province (ZHHY-2020-3).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data are not publicly available due to their containing information that could compromise the privacy of research participants.

**Acknowledgments:** The authors would like to thank the anonymous reviewers for their useful comments and careful reading of the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.
