Adversarial patrolling with spatially uncertain alarm signals

When securing complex infrastructures or large environments, constant surveillance of every area is not affordable. To cope with this issue, a common countermeasure is the usage of cheap but wide-ranged sensors, able to detect suspicious events that occur in large areas, supporting patrollers to improve the effectiveness of their strategies. However, such sensors are commonly affected by uncertainty. In the present paper, we focus on spatially uncertain alarm signals. That is, the alarm system is able to detect an attack but it is uncertain on the exact position where the attack is taking place. This is common when the area to be secured is wide such as in border patrolling and fair site surveillance. We propose, to the best of our knowledge, the first Patrolling Security Game model where a Defender is supported by a spatially uncertain alarm system which non-deterministically generates signals once a target is under attack. We show that finding the optimal strategy in arbitrary graphs is APX-hard even in zero-sum games and we provide two (exponential time) exact algorithms and two (polynomial time) approximation algorithms. Furthermore, we analyse what happens in environments with special topologies, showing that in linear and cycle graphs the optimal patrolling strategy can be found in polynomial time, de facto allowing our algorithms to be used in real-life scenarios, while in trees the problem is NP-hard. Finally, we show that without false positives and missed detections, the best patrolling strategy reduces to stay in a place, wait for a signal, and respond to it at best. This strategy is optimal even with non-negligible missed detection rates, which, unfortunately, affect every commercial alarm system. We evaluate our methods in simulation, assessing both quantitative and qualitative aspects.

Beaconing-Aware Optimal Policies for Two-Hop Routing in Multi-Class Delay Tolerant Networks

In Delay Tolerant Networks (DTNs), two-hop routing compromises energy versus delay more conveniently than epidemic routing. Literature provides comprehensive results on optimal routing policies for mobile nodes with homogeneous mobility, often neglecting signaling costs. Routing policies are customarily computed by means of fluid approximation techniques, which assure solutions to be optimal only when the number of nodes is infinite, while they provide a coarse approximation otherwise. This work addresses heterogeneous mobility patterns and multiple wireless transmission technologies; moreover, we explicitly consider the beaconing/signaling costs to support routing and the possibility for nodes to discard packets after a local time. We theoretically characterize the optimal policies by deriving their formal properties. Such analysis is leveraged to define two algorithmic approaches which allow to trade off optimality with computational efficiency. Theoretical bounds on the approximation guarantees of the proposed algorithms are derived. We then experimentally evaluated them in realistic scenarios of multi-class DTNs.

A Formal Framework for Mobile Robot Patrolling in Arbitrary Environments with Adversaries

Using mobile robots for autonomous patrolling of environments to prevent intrusions is a topic of increasing practical relevance. One of the most challenging scientific issues is the problem of finding effective patrolling strategies that, at each time point, determine the next moves of the patrollers in order to maximize some objective function. In the very last years this problem has been addressed in a game theoretical fashion, explicitly considering the presence of an adversarial intruder. The general idea is that of modeling a patrolling situation as a game, played by the patrollers and the intruder, and of studying the equilibria of this game to derive effective patrolling strategies. In this paper we present a game theoretical formal framework for the determination of effective patrolling strategies that extends the previous proposals appeared in the literature, by considering environments with arbitrary topology and arbitrary preferences for the agents. The main original contributions of this paper are the formulation of the patrolling game for generic graph environments, an algorithm for finding a deterministic equilibrium strategy, which is a fixed path through the vertices of the graph, and an algorithm for finding a non-deterministic equilibrium strategy, which is a set of probabilities for moving between adjacent vertices of the graph. Both the algorithms are analytically studied and experimentally validated, to assess their properties and efficiency.