Automated Abstractions for Patrolling Security Games

Recently, there has been a significant interest in studying security games to provide tools for addressing resource allocation problems in security applications. Patrolling security games (PSGs) constitute a special class of security games wherein the resources are mobile. One of the most relevant open problems in security games is the design of scalable algorithms to tackle realistic scenarios. While the literature mainly focuses on heuristics and decomposition techniques (e.g., double oracle), in this paper we provide, to the best of our knowledge, the first study on the use of abstractions in security games (specifically for PSGs) to design scalable algorithms. We define some classes of abstractions and we provide parametric algorithms to automatically generate abstractions. We show that abstractions allow one to relax the constraint of patrolling strategies' Markovianity (customary in PSGs) and to solve large game instances. We additionally pose the problem to search for the optimal abstraction and we develop an anytime algorithm to find it

Asynchronous Multi-Robot Patrolling against Intrusions in Arbitrary Topologies

Use of game theoretical models to derive randomized mobile robot patrolling strategies has recently received a growing attention. We focus on the problem of patrolling environments with arbitrary topologies using multiple robots. We address two important issues cur rently open in the literature. We determine the smallest number of robots needed to patrol a given environment and we compute the optimal patrolling strategies along several coordination dimensions. Finally, we experimentally evaluate the proposed techniques

Algorithms to Find Two-Hop Routing Policies in Multiclass Delay Tolerant Networks

Most of the literature on delay tolerant networks (DTNs) focuses on optimal routing policies exploiting a priori knowledge about nodes mobility traces. For the case in which no a priori knowledge is available (very common in practice), apart from basic epidemic routing, the main approaches focus on controlling two-hop routing policies. However, these latter results commonly employ fluid approximation techniques, which, in principle, do not provide any theoretical bound over the approximation ratio. In our work, we focus on the case without a priori mobility knowledge and we provide approximation algorithms with theoretical guarantees that can be applied to cases where the number of hops allowed in the routing process is arbitrary. Our approach is rather flexible allowing us to address heterogeneous mobility patterns and transmission technologies, to consider explicitly the signaling and transmission costs, and to include also nodes discarding packets after a local timeout. We then provide a comprehensive performance evaluation of our algorithms, showing that two-hop routing provides the best tradeoff between delay and energy and that, in this case, they find solutions very close to the optimal ones with a low overhead. Finally, we compare our methods against some state-of-the-art approaches by means of a DTN simulation environment in realistic settings

A Security Game Combining Patrolling and Alarm-Triggered Responses Under Spatial and Detection Uncertainties

Motivated by a number of security applications, among which border patrolling, we study, to the best of our knowledge, the first Security Game model in which patrolling strategies need to be combined with responses to signals raised by an alarm system, which is spatially uncertain (i.e., it is uncertain over the exact location the attack is ongoing) and is affected by false negatives (i.e., the missed detection rate of an attack may be positive). Ours is an infinite-horizon patrolling scenario on a graph, where a single patroller moves. We study the properties of the game model in terms of computational issues and form of the optimal strategies and we provide an approach to solve it. Finally, we provide an experimental analysis of our techniques

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 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 is FNP-hard even in tree graphs and APX-hard in arbitrary graphs. We provide two (exponential time) exact algorithms and two (polynomial time) approximation algorithms. 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