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November  2018, 1(4): 369-382. doi: 10.3934/mfc.2018018

## Relay selection based on social relationship prediction and information leakage reduction for mobile social networks

 1 School of Computer Science and Engineering, Changshu Institute of Technology, Changshu, China 2 Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, Suzhou, China 3 The School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China 4 Computer Science, The George Washington University, Washington DC, USA

* Corresponding author: Gaofei Sun

Received  July 2018 Revised  August 2018 Published  December 2018

Fund Project: The first author is supported by National Natural Science Foundation of China (61602062) and the Natural Science Foundation of Jiangsu Province (BK20160410)

Despite the extensive study on relay selection in mobile social networks (MSNs), few work has taken both transmission latency (i.e. efficiency) and information leakage probability (i.e. security) into consideration. Therefore we target on designing an efficient and secure relay selection algorithm to enable communication among legitimate users while reducing the information leakage probability to other users. In this paper, we propose a novel mobility model for MSN users considering both the randomness and the sociality of the movements, based on which the social relationship among users, i.e. the meeting probabilities among the users, are predicted. Taken both efficiency and security into consideration, we design a network formation game based relay selection algorithm by defining the payoff functions of the users, designing the game evolving rules, and proving the stability of the formed network structure. Extensive simulation is conducted to validate the performance of the relay selection algorithm by using both synthetic trace and real-world trace. The results show that our algorithm outperforms other algorithms by trading a balance between efficiency and security.

Citation: Xiaoshuang Xing, Gaofei Sun, Yong Jin, Wenyi Tang, Xiuzhen Cheng. Relay selection based on social relationship prediction and information leakage reduction for mobile social networks. Mathematical Foundations of Computing, 2018, 1 (4) : 369-382. doi: 10.3934/mfc.2018018
##### References:
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Zhang, Soroute: a reliable and effective social-based routing in cognitive radio ad hoc networks, EURASIP Journal on Wireless Communications and Networking, 2014 (2014), 200-214. doi: 10.1186/1687-1499-2014-200. Google Scholar [11] S. K. Kim, J. H. Yoon, J. Y. Lee, G. Y. Jang and S. B. Yang, A cooperative forwarding scheme for social preference-based selfishness in mobile social networks, Wireless Networks, 22 (2016), 537-552. doi: 10.1007/s11276-015-0984-2. Google Scholar [12] W. Li, X. Cheng, T. Jing and X. Xing, Cooperative multi-hop relaying via network formation games in cognitive radio networks, in IEEE INFOCOM, 2013, 971–979. doi: 10.1109/INFCOM.2013.6566886. Google Scholar [13] Y. Liang, Z. Cai, Q. Han and Y. Li, Location privacy leakage through sensory data, Security and Communication Networks, 2017 (2017), Article ID 7576307, 12 pages. doi: 10.1155/2017/7576307. Google Scholar [14] J. Lu, Z. Cai, X. Wang, L. Zhang, P. Li and Z. He, User social activity-based routing for cognitive radio networks, Personal and Ubiquitous Computing, 22 (2018), 471-487. doi: 10.1007/s00779-018-1114-9. Google Scholar [15] W. Moreira, P. Mendes and S. Sargento, Opportunistic routing based on daily routines, in IEEE WoWMoM, 2012, 1–6. doi: 10.1109/WoWMoM.2012.6263749. Google Scholar [16] L. Muchnik, S. Pei, L. C. Parra, S. D. S. Reis, J. S. Andrade Jr., S. Havlin and H. A. Makse, Origins of power-law degree distribution in the heterogeneity of human activity in social networks, Scientific Reports, 3.Google Scholar [17] I. Parris and F. Ben Abdesslem, Crawdad trace/social network analysis/st_andrews/locshare/2010/sta1, Downloaded from http://crawdad.org//download/st_andrews/locshare/locshare-StA1.tar.gz, Nov. 2010.Google Scholar [18] T. Spyropoulos, K. Psounis and C. Raghavendra, Efficient routing in intermittently connected mobile networks: The multiple-copy case, IEEE/ACM Transactions on Networking, 16 (2008), 77-90. doi: 10.1109/TNET.2007.897964. Google Scholar [19] A. Vahdat and D. Becker, Epidemic Routing for Partially-Connected ad Hoc Networks, Technical report, Duke University, 2000.Google Scholar [20] J. Wang, Z. Cai, Y. Li, D. Yang, J. Li and H. Gao, Protecting query privacy with differentially private k-anonymity in location-based services, Personal and Ubiquitous Computing, 1–17.Google Scholar [21] S. Wang, M. Liu, X. Cheng, Z. Li, J. Huang and B. Chen, Hero-a home based routing in pocket switched networks, in Proc. Wireless Algorithms, Systems, and Applications, 2012, 20–30. doi: 10.1007/978-3-642-31869-6_2. Google Scholar [22] J. Wu and Y. Wang, Social feature-based multi-path routing in delay tolerant networks, in Proc. IEEE INFOCOM, 2012, 1368–1376.Google Scholar [23] J. Wu, M. Xiao and L. Huang, Homing spread: Community home-based multi-copy routing in mobile social networks, in Proc. IEEE INFOCOM, 2013, 2319–2327.Google Scholar [24] X. Xing, T. Jing, W. Zhou, X. Cheng, Y. Huo and H. Liu, Routing in user-centric networks, IEEE Communications Magazine, 52 (2014), 44-51. Google Scholar [25] X. Zheng, Z. Cai, J. Li and H. Gao, Location-privacy-aware review publication mechanism for local business service systems, in IEEE INFOCOM, 2017. doi: 10.1109/INFOCOM.2017.8056976. Google Scholar [26] X. Zheng, Z. Cai and Y. Li, Data linkage in smart iot systems: A consideration from privacy perspective, IEEE Communications Magazine.Google Scholar [27] X. Zheng, Z. Cai, J. Yu, C. Wang and Y. Li, Follow but no track: Privacy preserved profile publishing in cyber-physical social systems, IEEE Internet of Things Journal, 4 (2017), 1868-1878. Google Scholar [28] X. Zheng, G. Luo and Z. Cai, A fair mechanism for private data publication in online social networks, IEEE Transactions on Network Science and Engineering.Google Scholar

show all references

##### References:
 [1] J. A. Bazerque and G. B. Giannakis, Distributed spectrum sensing for cognitive radio networks by exploiting sparsity, IEEE Transactions on Signal Processing, 58 (2010), 1847-1862. doi: 10.1109/TSP.2009.2038417. Google Scholar [2] Z. Cai, Z. He, X. Guan and Y. Li, Collective data-sanitization for preventing sensitive information inference attacks in social networks, IEEE Transactions on Dependable and Secure Computing, 15 (2018), 577-590. doi: 10.1109/TDSC.2016.2613521. Google Scholar [3] Z. Cai and X. Zheng, A private and efficient mechanism for data uploading in smart cyber-physical systems, IEEE Transactions on Network Science and Engineering.Google Scholar [4] W. Cheng, D. Wu, X. Cheng and D. Chen, Routing for information leakage reduction in multi-channel multi-hop ad-hoc social networks, Lecture Notes in Computer Science, 7405 (2012), 31-42. Google Scholar [5] R. Ciobanu, C. Dobre and V. Cristea, Sprint: Social prediction-based opportunistic routing, in IEEE WoWMoM, 2013, 1–7. doi: 10.1109/WoWMoM.2013.6583442. Google Scholar [6] V. Erramilli, M. Crovella, A. Chaintreau and C. Diot, Delegation forwarding, in Proc. MobiHoc, 2008, 251–260. doi: 10.1145/1374618.1374653. Google Scholar [7] Z. He, Z. Cai and J. Yu, Latent-data privacy preserving with customized data utility for social network data, IEEE Transactions on Vehicular Technology, 67 (2018), 665-673. Google Scholar [8] Z. He, Z. Cai, J. Yu, X. Wang, Y. Sun and Y. Li, Cost-efficient strategies for restraining rumor spreading in mobile social networks, IEEE Transactions on Vehicular Technology, 66 (2017), 2789-2800. doi: 10.1109/TVT.2016.2585591. Google Scholar [9] M. O. Jackson, A survey of models of network formation: Stability and efficiency, Cambridge University Press, (2010), 11–57. doi: 10.1017/CBO9780511614385.002. Google Scholar [10] T. Jing, J. Zhou, H. Liu and Z. Zhang, Soroute: a reliable and effective social-based routing in cognitive radio ad hoc networks, EURASIP Journal on Wireless Communications and Networking, 2014 (2014), 200-214. doi: 10.1186/1687-1499-2014-200. Google Scholar [11] S. K. Kim, J. H. Yoon, J. Y. Lee, G. Y. Jang and S. B. Yang, A cooperative forwarding scheme for social preference-based selfishness in mobile social networks, Wireless Networks, 22 (2016), 537-552. doi: 10.1007/s11276-015-0984-2. Google Scholar [12] W. Li, X. Cheng, T. Jing and X. Xing, Cooperative multi-hop relaying via network formation games in cognitive radio networks, in IEEE INFOCOM, 2013, 971–979. doi: 10.1109/INFCOM.2013.6566886. Google Scholar [13] Y. Liang, Z. Cai, Q. Han and Y. Li, Location privacy leakage through sensory data, Security and Communication Networks, 2017 (2017), Article ID 7576307, 12 pages. doi: 10.1155/2017/7576307. Google Scholar [14] J. Lu, Z. Cai, X. Wang, L. Zhang, P. Li and Z. He, User social activity-based routing for cognitive radio networks, Personal and Ubiquitous Computing, 22 (2018), 471-487. doi: 10.1007/s00779-018-1114-9. Google Scholar [15] W. Moreira, P. Mendes and S. Sargento, Opportunistic routing based on daily routines, in IEEE WoWMoM, 2012, 1–6. doi: 10.1109/WoWMoM.2012.6263749. Google Scholar [16] L. Muchnik, S. Pei, L. C. Parra, S. D. S. Reis, J. S. Andrade Jr., S. Havlin and H. A. Makse, Origins of power-law degree distribution in the heterogeneity of human activity in social networks, Scientific Reports, 3.Google Scholar [17] I. Parris and F. Ben Abdesslem, Crawdad trace/social network analysis/st_andrews/locshare/2010/sta1, Downloaded from http://crawdad.org//download/st_andrews/locshare/locshare-StA1.tar.gz, Nov. 2010.Google Scholar [18] T. Spyropoulos, K. Psounis and C. Raghavendra, Efficient routing in intermittently connected mobile networks: The multiple-copy case, IEEE/ACM Transactions on Networking, 16 (2008), 77-90. doi: 10.1109/TNET.2007.897964. Google Scholar [19] A. Vahdat and D. Becker, Epidemic Routing for Partially-Connected ad Hoc Networks, Technical report, Duke University, 2000.Google Scholar [20] J. Wang, Z. Cai, Y. Li, D. Yang, J. Li and H. Gao, Protecting query privacy with differentially private k-anonymity in location-based services, Personal and Ubiquitous Computing, 1–17.Google Scholar [21] S. Wang, M. Liu, X. Cheng, Z. Li, J. Huang and B. Chen, Hero-a home based routing in pocket switched networks, in Proc. Wireless Algorithms, Systems, and Applications, 2012, 20–30. doi: 10.1007/978-3-642-31869-6_2. Google Scholar [22] J. Wu and Y. Wang, Social feature-based multi-path routing in delay tolerant networks, in Proc. IEEE INFOCOM, 2012, 1368–1376.Google Scholar [23] J. Wu, M. Xiao and L. Huang, Homing spread: Community home-based multi-copy routing in mobile social networks, in Proc. IEEE INFOCOM, 2013, 2319–2327.Google Scholar [24] X. Xing, T. Jing, W. Zhou, X. Cheng, Y. Huo and H. Liu, Routing in user-centric networks, IEEE Communications Magazine, 52 (2014), 44-51. Google Scholar [25] X. Zheng, Z. Cai, J. Li and H. Gao, Location-privacy-aware review publication mechanism for local business service systems, in IEEE INFOCOM, 2017. doi: 10.1109/INFOCOM.2017.8056976. Google Scholar [26] X. Zheng, Z. Cai and Y. Li, Data linkage in smart iot systems: A consideration from privacy perspective, IEEE Communications Magazine.Google Scholar [27] X. Zheng, Z. Cai, J. Yu, C. Wang and Y. Li, Follow but no track: Privacy preserved profile publishing in cyber-physical social systems, IEEE Internet of Things Journal, 4 (2017), 1868-1878. Google Scholar [28] X. Zheng, G. Luo and Z. Cai, A fair mechanism for private data publication in online social networks, IEEE Transactions on Network Science and Engineering.Google Scholar
A toy example of user $i$'s movement
The power law distribution under different $k$
Performance comparison in the real trace. (a) Comparing the A-Latency performance. (b) Comparing the A-MLP performance
Simulation Settings
 Parameter Meaning Setting $k_r$ The exponent of the power law distribution for $\zeta_{i\tau}$ 1.7 $k_l$ The exponent of the power law distribution for $p_i$ 3 $C_l$ The maximum value of $p_i$ 0.6 $R_d$ The radius of the communication range 6m $\epsilon$ The length of the time interval within which users keep their moving direction and speed unchanged 30s $\mu$ The mean of the normal distribution for users' speed 1.4 $\sigma$ The standard deviation of the normal distribution for users' speed $\frac{\mu}{3}$
 Parameter Meaning Setting $k_r$ The exponent of the power law distribution for $\zeta_{i\tau}$ 1.7 $k_l$ The exponent of the power law distribution for $p_i$ 3 $C_l$ The maximum value of $p_i$ 0.6 $R_d$ The radius of the communication range 6m $\epsilon$ The length of the time interval within which users keep their moving direction and speed unchanged 30s $\mu$ The mean of the normal distribution for users' speed 1.4 $\sigma$ The standard deviation of the normal distribution for users' speed $\frac{\mu}{3}$
Simulation Results
 ESRS Relation Leakage Rand A-Latency 16.2 15.4 17.9 30.4 A-MLP 0.38 0.63 0.35 0.72
 ESRS Relation Leakage Rand A-Latency 16.2 15.4 17.9 30.4 A-MLP 0.38 0.63 0.35 0.72
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