Adversarial patrolling with spatially uncertain alarm signals

Basilico, Nicola; Nittis, Giuseppe De; Gatti, Nicola

doi:10.1016/j.artint.2017.02.007

Cited by 28 publications

(26 citation statements)

References 27 publications

(53 reference statements)

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“…Here the independent set is {1, 5, 9} , and the covering intervals are [1,3] , [4,6] and [7,9] , as shown in Figure 5. So the attacks are equiprobable on the independent set (denoted by x below) and the Patroller oscillates equiprobably on the three stated intervals.…”

Section: Proofmentioning

confidence: 99%

Patrolling a Border

Papadaki¹,

Alpern²,

Lidbetter³

et al. 2016

Operations Research

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Patrolling games were recently introduced by Alpern, Morton and Papadaki to model the problem of protecting the nodes of a network from an attack. Time is discrete and in each time unit the Patroller can stay at the same node or move to an adjacent node. The Attacker chooses when to attack and which node to attack, and needs m consecutive time units to carry it out. The Attacker wins if the Patroller does not visit the chosen node while it is being attacked; otherwise the Patroller wins. This paper studies the patrolling game where the network is a line graph of n nodes, which models the problem of guarding a channel or protecting a border from infiltration. We solve the patrolling game for any values of m and n, providing an optimal Patroller strategy, an optimal Attacker strategy and the value of the game (optimal probability that the attack is intercepted).

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Section: Proofmentioning

confidence: 99%

Patrolling a Border

Papadaki¹,

Alpern²,

Lidbetter³

et al. 2016

Operations Research

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“…[4] Algorithm multi-LP spatial branch-and-bound [6] multi-lex-MILP -optimistic version) in structured games where the action space is combinatorial. See [7] for more references.…”

Section: Previous Workmentioning

confidence: 99%

“…Notice that degenerate sets D p (a −n , a p ) play no role in Problem (7). This is because if D p (a −n , a p ) is degenerate, its constraint a n ∈A n U a −n ,a n p…”

Section: Theorem 5 Let ψ(Xmentioning

confidence: 99%

Computing a Pessimistic Stackelberg Equilibrium with Multiple Followers: The Mixed-Pure Case

2019

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The search problem of computing a Stackelberg (or leader-follower) equilibrium (also referred to as an optimal strategy to commit to) has been widely investigated in the scientific literature in, almost exclusively, the single-follower setting. Although the optimistic and pessimistic versions of the problem, i.e., those where the single follower breaks any ties among multiple equilibria either in favour or against the leader, are solved with different methodologies, both cases allow for efficient, polynomialtime algorithms based on linear programming. The situation is different with multiple followers, where results are only sporadic and depend strictly on the nature of the followers' game. In this paper, we investigate the setting of a normal-form game with a single leader and multiple followers who, after observing the leader's commitment, play a Nash equilibrium. When both leader and followers are allowed to play mixed strategies, the corresponding search problem, both in the optimistic and pessimistic versions, is known to be inapproximable in polynomial time to within any multiplicative polynomial factor unless P = NP. Exact algorithms are known only for the optimistic case. We focus on the case where the followers play pure strategies-a restriction that applies to a number of real-world scenarios and which, in principle, makes the problem easier-under the assumption of pessimism (the optimistic version of the problem can be straightforwardly solved in polynomial time). After casting this search problem (with followers playing pure strategies) as a pessimistic bilevel programming problem, we show that, with two followers, the problem is NP-hard and, with three or more followers, it cannot be approximated in polynomial time to within any multiplicative factor which is polynomial in the size of the normal-form game, nor, assuming utilities in [0, 1], to within any constant additive loss stricly smaller than 1 unless P = NP. This shows that, differently from what happens in the optimistic version, hardness and inapproximability in the pessimistic problem are not due to the adoption of mixed strategies. We then show that the problem admits, in the general case, a supremum but not a maximum, and we propose a single-level mathematical programming reformulation which asks for the maximization of a nonconcave All the authors contributed equally to this manuscript. Extended author information available on the last page of the article quadratic constraints. Since, due to admitting a supremum but not a maximum, only a restricted version of this formulation can be solved to optimality with state-of-theart methods, we propose an exact ad hoc algorithm (which we also embed within a branch-and-bound scheme) capable of computing the supremum of the problem and, for cases where there is no leader's strategy where such value is attained, also an α-approximate strategy where α > 0 is an arbitrary additive loss (at most as large as the supremum). We conclude the paper by evaluating the scalability of our algorithms via computat...

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“…Due to the increasing threats of terroristic and criminal behaviors in the present world, researchers have developed lots of intelligent surveillance systems, such as suspect object tracking, intrusion detection, indoor security systems, traffic safety analysis, antisocial behavior analysis, and so on. The primary aim of these studies is to develop security system that can detect and predict the potential threats of objects being watched according to a large collection of meaningful events that are derived from sensory data of dispersed sources.…”

Section: Introductionmentioning

confidence: 99%

A Dempster‐Shafer theory and uninorm‐based framework of reasoning and multiattribute decision‐making for surveillance system

Liu

Luo

et al. 2019

Int J Intell Syst

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Closed-circuit television and sensor-based intelligent surveillance systems have attracted considerable attentions in the field of public security affairs. To provide real-time reaction in the case of a huge volume of the surveillance data, researchers have proposed eventreasoning frameworks for modeling and inferring events of interest. However, they do not support decisionmaking, which is very important for surveillance operators. To this end, this paper incorporate a function of decision-making in an event-reasoning framework, so that our model not only can perform event-reasoning but also can predict, rank, and alarm threats according to uncertain information from multiple heterogeneous sources. In particular, we propose a multiattribute decision-making model, in which an object being watched is modeled as a multiattribute event, where each attribute corresponds to a specific source, and the information from each source can be used to elicit a local threat degree of different malicious situations with respect to the corresponding attribute. Moreover, to assess an overall threat degree of an object being observed, we also propose a method to fuse the conflict threat degrees regarding all the relevant attributes.

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Adversarial patrolling with spatially uncertain alarm signals

Cited by 28 publications

References 27 publications

Patrolling a Border

Patrolling a Border

Computing a Pessimistic Stackelberg Equilibrium with Multiple Followers: The Mixed-Pure Case

A Dempster‐Shafer theory and uninorm‐based framework of reasoning and multiattribute decision‐making for surveillance system

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