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  1. In recent years, Internet of Things (IoT) devices have been extensively deployed in edge networks, including smart homes and offices. Despite the exciting opportunities afforded by the advancements in the IoT, it also introduces new attack vectors and vulnerabilities in the system. Existing studies have shown that the attack graph is an effective model for performing system-level analysis of IoT security. In this paper, we study IoT system vulnerability analysis and network hardening. We first extend the concept of attack graph to weighted attack graph and design a novel algorithm for computing a shortest attack trace in a weighted attack graph. We then formulate the network hardening problem. We prove that this problem is NP-hard, and then design an exact algorithm and a heuristic algorithm to solve it. Extensive experiments on 9 synthetic IoT systems and 2 real-world smart home IoT testbeds demonstrate that our shortest attack trace algorithm is robust and fast, and our heuristic network hardening algorithm is efficient in producing near optimal results compared to the exact algorithm. 
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  2. In this paper, we study the properties of path metrics of an entanglement path for a given entanglement swapping order of the path. We show how to efficiently compute the path metrics of an entanglement path for any given swapping order. We show that different entanglement swapping orders for the same path can lead to different expected throughputs. A key finding is that the binary operator corresponding to entanglement swapping along a path is not associative. We further show that the problem of computing an s-t path with maximum expected throughput under any entanglement swapping order does not have the subpath optimality property, which is a key property most path finding algorithms such as Dijkstra’s algorithm rely on. We use extensive simulations to validate our theoretical findings. 
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