Interdiction Models and Applications

Dimitrov, Nedialko B.; Morton, David P.

doi:10.1007/978-1-4614-5278-2_4

Cited by 12 publications

(9 citation statements)

References 44 publications

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“…Models that explicitly take into account the strategic nature of the adversary lead to game theory models, which include network interdiction problems, [12], and patrolling games over networks, [2]. In particular, in [24], the authors determine the optimal patroling strategy on a border by considering a zero sum simultaneous game over a line network.…”

Section: Literature Reviewmentioning

confidence: 99%

Coordinating resources in Stackelberg Security Games

Bucarey

Casorrán²,

Ordóñez³

et al. 2021

European Journal of Operational Research

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In this work we formulate a Stackelberg Security Game that coordinates resources in a border patrol problem. In this security domain, resources from different precincts have to be paired to conduct patrols in the border due to logistic constraints. Given this structure, models that enumerate the pure defender strategies scale poorly. We describe the set of mixed strategies using a polynomial number of variables but exponentially many constraints that come from the matching polytope. We then include this description in a mixed integer formulation to compute the Strong Stackelberg Equilibrium efficiently with a branch and cut scheme. Since the optimal patrol solution is a probability distribution over the set of exponential size, we also introduce an efficient sampling method that can be used to deploy the security resources every shift. Our computational results evaluate the efficiency of the branch and cut scheme developed and the accuracy of the sampling method.

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Section: Literature Reviewmentioning

confidence: 99%

Coordinating resources in Stackelberg Security Games

Bucarey

Casorrán²,

Ordóñez³

et al. 2021

European Journal of Operational Research

View full text Add to dashboard Cite

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“…Network interdiction models tend to follow the process outlined by Smith (2008). Dimitrov and Morton (2013) describe four applications of network interdiction modeling, including one that is similar to the case study model, in this work: identifying vulnerabilities in an electric power system. Work that utilized the notion of network interdiction for analyzing source-destination path availability in a network infrastructure was conducted by Murray, et al (2007) and Matisziw and Murray (2009).…”

Section: Network Interdiction Modelingmentioning

confidence: 99%

Promoting Resiliency in Emergency Communication Networks

Bartolacci

Dimitrov

2017

International Journal of Information Systems for Crisis Response and Management

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Police, fire, and emergency personnel rely on wireless networks to serve the public. Whether it is during a natural disaster, or just an ordinary calendar day, wireless nodes of varying types form the infrastructure that local, regional, and even national scale agencies use to communicate while keeping the population served safe and secure. In this article, Michael R. Bartolacci and Stanko Dimitrov present a network interdiction modeling approach that can be utilized for analyzing vulnerabilities in public service wireless networks; subject to hacking, terrorism, or destruction from natural disasters. They develop a case study for wireless networks utilized by the sheriff's department of Miami-Dade County in Florida in the United States. Finally, the authors' modeling approach—given theoretical budgets for the “hardening” of wireless network nodes and for would-be destroyers of such nodes—highlights parts of the network where further investment may prevent damage and loss of capacity.

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“…Given a graph G with n nodes, a regression task on graphstructured data based on G consists of approximating a function F : Ω ⊆R n → R m , m ≤ n, depending on the adjacency matrix of G, and that returns the m values related to a fixed subset of m nodes for each set of values assigned to the nodes of G. This type of regression task has applications in many interesting fields, such as circulation with demand (CwD) problems (see [chap. 7.7] in [14]), network interdiction models (NIMs) [15], and flux regression problems in underground fractured media [16,17]. A classic multi-layer perceptron (MLP), or its suitable variants, can perform this regression task on the graph data with a good performance [16,17], implicitly learning the node relationships during the training (see [18,19]).…”

Section: Introductionmentioning

confidence: 99%

Graph-Informed Neural Networks for Regressions on Graph-Structured Data

et al. 2022

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In this work, we extend the formulation of the spatial-based graph convolutional networks with a new architecture, called the graph-informed neural network (GINN). This new architecture is specifically designed for regression tasks on graph-structured data that are not suitable for the well-known graph neural networks, such as the regression of functions with the domain and codomain defined on two sets of values for the vertices of a graph. In particular, we formulate a new graph-informed (GI) layer that exploits the adjacent matrix of a given graph to define the unit connections in the neural network architecture, describing a new convolution operation for inputs associated with the vertices of the graph. We study the new GINN models with respect to two maximum-flow test problems of stochastic flow networks. GINNs show very good regression abilities and interesting potentialities. Moreover, we conclude by describing a real-world application of the GINNs to a flux regression problem in underground networks of fractures.

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Interdiction Models and Applications

Cited by 12 publications

References 44 publications

Coordinating resources in Stackelberg Security Games

Coordinating resources in Stackelberg Security Games

Promoting Resiliency in Emergency Communication Networks

Graph-Informed Neural Networks for Regressions on Graph-Structured Data

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