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  1. The increasing penetration of cyber systems into smart grids has resulted in these grids being more vulnerable to cyber physical attacks. The central challenge of higher order cyber-physical contingency analysis is the exponential blow-up of the attack surface due to a large number of attack vectors. This gives rise to computational challenges in devising efficient attack mitigation strategies. However, a system operator can leverage private information about the underlying network to maintain a strategic advantage over an adversary equipped with superior computational capability and situational awareness. In this work, we examine the following scenario: A malicious entity intrudes the cyber-layer of a power network and trips the transmission lines. The objective of the system operator is to deploy security measures in the cyber-layer to minimize the impact of such attacks. Due to budget constraints, the attacker and the system operator have limits on the maximum number of transmission lines they can attack or defend. We model this adversarial interaction as a resource-constrained attacker-defender game. The computational intractability of solving large security games is well known. However, we exploit the approximately modular behavior of an impact metric known as the disturbance value to arrive at a linear-time algorithm for computing an optimal defense strategy. We validate the efficacy of the proposed strategy against attackers of various capabilities and provide an algorithm for a real-time implementation. 
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  2. In this work, we investigate a security game between an attacker and a defender, originally proposed in [6]. As is well known, the combinatorial nature of security games leads to a large cost matrix. Therefore, computing the value and optimal strategy for the players becomes computationally expensive. In this work, we analyze a special class of zero-sum games in which the payoff matrix has a special structure which results from the additive property of the utility function. Based on variational principles, we present structural properties of optimal attacker as well as defender’s strategy. We propose a linear-time algorithm to compute the value based on the structural properties, which is an improvement from our previous result in [6], especially in the context of large-scale zero-sum games. 
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