Abstract
The privacy and security of the Internet of Things (IoT) are emerging as popular issues in the IoT. At present, there exist several pieces of research on network analysis on the IoT network, and malicious network analysis may threaten the privacy and security of the leader in the IoT networks. With this in mind, we focus on how to avoid malicious network analysis by modifying the topology of the IoT network and we choose closeness centrality as the network analysis tool. This paper makes three key contributions toward this problem: (1) An optimization problem of removing k edges to minimize (maximize) the closeness value (rank) of the leader; (2) A greedy (greedy and simulated annealing) algorithm to solve the closeness value (rank) case of the proposed optimization problem in polynomial time; and (3)UpdateCloseness (FastTopRank)—algorithm for computing closeness value (rank) efficiently. Experimental results prove the efficiency of our pruning algorithms and show that our heuristic algorithms can obtain accurate solutions compared with the optimal solution (the approximation ratio in the worst case is 0.85) and outperform the solutions obtained by other baseline algorithms (e.g., choose k edges with the highest degree sum).
Highlights
Due to the fact that we find that only greedy algorithm cannot obtain a (1 − 1e ) approximation ratio like the value case, we exploit simulated annealing algorithm which takes greedy solution as an initial solution for the purpose of converging faster to a better solution in less time and the detail of simulated annealing algorithm is shown in Algorithm 5
Our FastTopRank algorithm can significantly reduce the times of breadth-first search (BFS), i.e., k n when asserting the rank of top nodes
The budget of the removed edges k ranges from 1 to 5 and we proposed the notation of minimum approximation ratio as the worst case in every budget k and it presents the ratio between the greedy solution and the optimal solution Table 5 shows the Min Appro Ratio of each network and we discover that the worst case of our approximate greedy algorithm is far more accurate than the theorical lower bound (1 − 1e ≈ 0.63)
Summary
Centrality analysis, a kind of network analysis tool, has been applied in the area of Internet of Things (IoT) and can be used to analyze the topology of the IoT network. Closeness centrality [4] is chosen as the measurement of the importance of the nodes in the IoT network and leader (the protected target of our work) is the node that has the highest closeness value in the network. The leader often has the greatest impact on other nodes or has the clearest understanding of the network [5] and it is vulnerable to be analyzed and attacked by attackers Against this background, to guarantee individual privacy and cyber security, we attempt to Sensors 2019, 19, 3886; doi:10.3390/s19183886 www.mdpi.com/journal/sensors. Sensors 2019, 19, 3886 solve the above problem by removing limited links in the network to help the leader not be found by the attackers who use the closeness centrality analysis. To evade attacker’s analysis, the leader needs to remove limited links in the network (guaranteeing the connectivity of the network) and minimize (maximize) its closeness value (rank). The above problem is considered to be an optimization problem: “ How to minimize (maximize) the closeness value (rank) of the leader by removing k edges ? ”
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