Securing a border under asymmetric information

Sullivan, Kelly M.; Morton, David P.; Pan, Feng; Smith, J. Cole

doi:10.1002/nav.21567

Cited by 33 publications

(18 citation statements)

References 10 publications

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“…Stochastic network interdiction problems incorporate uncertainties that often arise in adversarial attacks (Cormican, Morton, & Wood, ). Stochastic network interdiction problems have various applications such as detecting smuggled nuclear material at borders (Sullivan, Morton, Pan, & Cole Smith, ) and interdicting drug transportation networks (Pan & Morton, ). The stochasticity often occurs in network parameters such as arc capacities and interdiction attempts.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Lei, Shen, and Song () propose a min‐max flow problem, where the interdictor's action for each arc is random with a given success rate in reducing the arc's capacity. Multiple solution approaches have been used to solve these problems such as L‐shaped method (Pan & Morton, ), cutting‐planes (Sullivan et al, ), decomposition methods (Held, Hemmecke, & Woodruff, ; Janjarassuk & Linderoth, ), sample average approximation (Lei et al, ; Song & Shen, ).…”

Section: Literature Reviewmentioning

confidence: 99%

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Interdiction models for delaying adversarial attacks against critical information technology infrastructure

Zheng

Albert

2019

Naval Research Logistics

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Information technology (IT) infrastructure relies on a globalized supply chain that is vulnerable to numerous risks from adversarial attacks. It is important to protect IT infrastructure from these dynamic, persistent risks by delaying adversarial exploits. In this paper, we propose max‐min interdiction models for critical infrastructure protection that prioritizes cost‐effective security mitigations to maximally delay adversarial attacks. We consider attacks originating from multiple adversaries, each of which aims to find a “critical path” through the attack surface to complete the corresponding attack as soon as possible. Decision‐makers can deploy mitigations to delay attack exploits, however, mitigation effectiveness is sometimes uncertain. We propose a stochastic model variant to address this uncertainty by incorporating random delay times. The proposed models can be reformulated as a nested max‐max problem using dualization. We propose a Lagrangian heuristic approach that decomposes the max‐max problem into a number of smaller subproblems, and updates upper and lower bounds to the original problem via subgradient optimization. We evaluate the perfect information solution value as an alternative method for updating the upper bound. Computational results demonstrate that the Lagrangian heuristic identifies near‐optimal solutions efficiently, which outperforms a general purpose mixed‐integer programming solver on medium and large instances.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Interdiction models for delaying adversarial attacks against critical information technology infrastructure

Zheng

Albert

2019

Naval Research Logistics

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“…Since these early developments there has been a flurry of interest and publications on this subject, partly due to its captivating combinatorial nature, and partly due to many applications including those in warfare , flood control , spread of contagious diseases , filtering or chemically treating toxic waste , identification of “critical infrastructure” , intercepting drug, weapons, nuclear material smuggling , and computer network monitoring .…”

Section: Introductionmentioning

confidence: 99%

“…These problems can further be divided into different classes based on for example, node or arc removal , complete or partial interdiction , single or multicommodity flow , single or multiobjective , deterministic or stochastic and randomized interdiction , and symmetry or asymmetry of information .…”

Section: Introductionmentioning

confidence: 99%

Two extended formulations for cardinality maximum flow network interdiction problem

Rad

Kakhki

2017

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We consider the maximum flow network interdiction problem in its cardinality case. There is an integer programming model for this problem by Wood (Math Comput Model 17 (1993), 1–18). Two types of valid inequalities have also been proposed (Altner et al., Oper Res Lett 38 (2010), 33–38 and Wood, Math Comput Model 17 (1993), 1–18) to strengthen the LP relaxation of the integer model. However, due to their combinatorial nature, the number of these inequalities are exponential. Here, we present an equivalent reformulation (extended formulation) for this problem which has a polynomial number of constraints. We also introduce new valid inequalities, and show that the corresponding reformulation of the LP relaxation of the integer model augmented with these inequalities, significantly decreases the integrality gap for a class of network interdiction problems with proven large integrality gaps. Numerical results for some benchmark as well as randomly generated instances are also reported. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 69(4), 367–377 2017

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“…Bailey et al [6] model a problem that has both of these types of uncertainty. Information asymmetry between interdictor and opponent has been studied [11,27,37,41,42] as have multiple-objective problems [35][36][37]. Applications of interdiction models vary widely, including infection control [5], natural disaster mitigation [43], military tactic development [10], natural resource and infrastructure security [11,38,39,44], and prevention of nuclear proliferation [12,27,32].…”

Section: Introductionmentioning

confidence: 99%

Exact algorithms for solving a Euclidean maximum flow network interdiction problem

Sullivan

Smith

2014

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We consider an interdiction problem that involves an operator (or defender) whose goal is to maximize flow from a source node to a sink node in some network that resides in Euclidean space. The problem we examine takes the perspective of an interdictor, who seeks to minimize the defender's maximum flow by locating a set of attacks that diminish arc capacities in accordance with the distance from the arc to the attack. Attacks are not restricted to node or arc locations, and can occur anywhere on the region in which the network is located. We refer to this problem as the Euclidean maximum flow network interdiction problem (E‐MFNIP). We show that E‐MFNIP is NP‐hard, as it generalizes the maximum flow interdiction problem studied by Wood . This article contributes two approaches to solving E‐MFNIP based on solving a sequence of lower‐bounding integer programs from which upper bounds can be readily obtained, and shows that these bounds are convergent. Computations on a set of test instances indicate that an approach based on space‐discretization tends to converge much faster than one based on linearizing the nonlinear capacity functions. We demonstrate the application of our space‐discretization approach on a real geographical network. © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 64(2), 109–124 2014

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Securing a border under asymmetric information

Cited by 33 publications

References 10 publications

Interdiction models for delaying adversarial attacks against critical information technology infrastructure

Interdiction models for delaying adversarial attacks against critical information technology infrastructure

Two extended formulations for cardinality maximum flow network interdiction problem

Exact algorithms for solving a Euclidean maximum flow network interdiction problem

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