Interdiction of a Markovian Evader

Gutfraind, Alexander; Hagberg, Aric; Izraelevitz, David; Pan, Feng

doi:10.1287/ics.2011.0020

Cited by 10 publications

(14 citation statements)

References 19 publications

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“…In examples discussed above, much of the challenge in interdiction stems from the unpredictability of evader motion. Our approach is to use a stochastic evader model to capture this unpredictability [6,10]. We assume that an evader is traveling from a source node s to a target node t on a graph G(N, E) according to a guided random walk defined by the Markovian transition matrix M; from node i the evader travels on edge (i, j) with probability M i j .…”

Section: Evadersmentioning

confidence: 99%

“…We assume that an evader is traveling from a source node s to a target node t on a graph G(N, E) according to a guided random walk defined by the Markovian transition matrix M; from node i the evader travels on edge (i, j) with probability M i j . The transition probabilities can be derived, for example, from the cost and risk of traversing an edge [10].…”

Section: Evadersmentioning

confidence: 99%

“…(4). If the matrix M has special structure then it could be reduced to O(|N| 2 ) [10] or even faster. We will use this evader model in the simulations, but in general the methods of Secs.…”

Section: Objective Functionmentioning

confidence: 99%

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Optimal Interdiction of Unreactive Markovian Evaders

Gutfraind

Hagberg

Pan

2009

Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems

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The interdiction problem arises in a variety of areas including military logistics, infectious disease control, and counter-terrorism. In the typical formulation of network interdiction, the task of the interdictor is to find a set of edges in a weighted network such that the removal of those edges would maximally increase the cost to an evader of traveling on a path through the network. Our work is motivated by cases in which the evader has incomplete information about the network or lacks planning time or computational power, e.g. when authorities set up roadblocks to catch bank robbers, the criminals do not know all the roadblock locations or the best path to use for their escape. We introduce a model of network interdiction in which the motion of one or more evaders is described by Markov processes and the evaders are assumed not to react to interdiction decisions. The interdiction objective is to find an edge set of size B, that maximizes the probability of capturing the evaders. We prove that similar to the standard least-cost formulation for deterministic motion this interdiction problem is also NP-hard. But unlike that problem our interdiction problem is submodular and the optimal solution can be approximated within 1 − 1/e using a greedy algorithm. Additionally, we exploit submodularity through a priority evaluation strategy that eliminates the linear complexity scaling in the number of network edges and speeds up the solution by orders of magnitude. Taken together the results bring closer the goal of finding realistic solutions to the interdiction problem on global-scale networks. 1

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Section: Evadersmentioning

confidence: 99%

Section: Evadersmentioning

confidence: 99%

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Optimal Interdiction of Unreactive Markovian Evaders

Gutfraind

Hagberg

Pan

2009

Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems

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“…The problems analyzed here belong to a large class of discrete optimization problems, collectively termed Network Interdiction [4, 14, 24, 28]. They are motivated by applications such as supply chains, electronic sensing, and counter-terrorism and relate to classical optimization problems like Set Cover and Max Coverage.…”

Section: Introductionmentioning

confidence: 99%

“…Such evaders are reactive in the sense that the routes they take are modified based on the set of available edges or nodes. In [14], an intermediate model was studied in which the evader follows a parametrized generalization of shortest path and random walk.…”

Section: Introductionmentioning

confidence: 99%

Evader interdiction: algorithms, complexity and collateral damage

2013

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In network interdiction problems, evaders (e.g., hostile agents or data packets) are moving through a network toward targets and we wish to choose locations for sensors in order to intercept the evaders. The evaders might follow deterministic routes or Markov chains, or they may be reactive, i.e., able to change their routes in order to avoid the sensors. The challenge in such problems is to choose sensor locations economically, balancing interdiction gains with costs, including the inconvenience sensors inflict upon innocent travelers. We study the objectives of (1) maximizing the number of evaders captured when limited by a budget on sensing cost and, (2) capturing all evaders as cheaply as possible. We give algorithms for optimal sensor placement in several classes of special graphs and hardness and approximation results for general graphs, including evaders who are deterministic, Markov chain-based, reactive and unreactive. A similar-sounding but fundamentally different problem setting was posed by Glazer and Rubinstein where both evaders and innocent travelers are reactive. We again give optimal algorithms for special cases and hardness and approximation results on general graphs.

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Evader Interdiction and Collateral Damage

Johnson

Gutfraind

2012

Algorithms for Sensor Systems

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In network interdiction problems, evaders (e.g., hostile agents or data packets) may be moving through a network towards targets and we wish to choose locations for sensors in order to intercept the evaders before they reach their destinations. The evaders might follow deterministic routes or Markov chains, or they may be reactive, i.e., able to change their routes in order to avoid sensors placed to detect them. The challenge in such problems is to choose sensor locations economically, balancing security gains with costs, including the inconvenience sensors inflict upon innocent travelers. We study the objectives of 1) maximizing the number of evaders captured when limited by a budget on sensing cost and 2) capturing all evaders as cheaply as possible. We give optimal sensor placement algorithms for several classes of special graphs and hardness and approximation results for general graphs, including for deterministic or Markov chain-based and reactive or oblivious evaders. In a similar-sounding but fundamentally different problem setting posed by [7] where both evaders and innocent travelers are reactive, we again give optimal algorithms for special cases and hardness and approximation results on general graphs.

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Interdiction of a Markovian Evader

Cited by 10 publications

References 19 publications

Optimal Interdiction of Unreactive Markovian Evaders

Optimal Interdiction of Unreactive Markovian Evaders

Evader interdiction: algorithms, complexity and collateral damage

Evader Interdiction and Collateral Damage

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