Cops and Invisible Robbers: the Cost of Drunkenness

We examine a version of the Cops and Robber (CR) game in which the robber is invisible, i.e., the cops do not know his location until they capture him. Apparently this game (CiR) has received little attention in the CR literature. We examine two variants: in the first the robber is adversarial (he actively tries to avoid capture); in the second he is drunk (he performs a random walk). Our goal in this paper is to study the invisible Cost of Drunkenness (iCOD), which is defined as the ratio ct_i(G)/dct_i(G), with ct_i(G) and dct_i(G) being the expected capture times in the adversarial and drunk CiR variants, respectively. We show that these capture times are well defined, using game theory for the adversarial case and partially observable Markov decision processes (POMDP) for the drunk case. We give exact asymptotic values of iCOD for several special graph families such as $d$-regular trees, give some bounds for grids, and provide general upper and lower bounds for general classes of graphs. We also give an infinite family of graphs showing that iCOD can be arbitrarily close to any value in [2,infinty). Finally, we briefly examine one more CiR variant, in which the robber is invisible and "infinitely fast"; we argue that this variant is significantly different from the Graph Search game, despite several similarities between the two games

Search and Pursuit-Evasion in Mobile Robotics, A survey

This paper surveys recent results in pursuitevasion and autonomous search relevant to applications in mobile robotics. We provide a taxonomy of search problems that highlights the differences resulting from varying assumptions on the searchers, targets, and the environment. We then list a number of fundamental results in the areas of pursuit-evasion and probabilistic search, and we discuss field implementations on mobile robotic systems. In addition, we highlight current open problems in the area and explore avenues for future work

Hyperopic Cops and Robbers

International audienceWe introduce a new variant of the game of Cops and Robbers played on graphs, where the robber is invisible unless outside the neighbor set of a cop. The hyperopic cop number is the corresponding analogue of the cop number, and we investigate bounds and other properties of this parameter. We characterize the cop-win graphs for this variant, along with graphs with the largest possible hyperopic cop number. We analyze the cases of graphs with diameter 2 or at least 3, focusing on when the hyperopic cop number is at most one greater than the cop number. We show that for planar graphs, as with the usual cop number, the hyperopic cop number is at most 3. The hyperopic cop number is considered for countable graphs, and it is shown that for connected chains of graphs, the hyperopic cop density can be any real number in [0, 1/2]

Graph-theoretic Approach To Modeling Propagation And Control Of Network Worms

In today\u27s network-dependent society, cyber attacks with network worms have become the predominant threat to confidentiality, integrity, and availability of network computing resources. Despite ongoing research efforts, there is still no comprehensive network-security solution aimed at controling large-scale worm propagation. The aim of this work is fivefold: (1) Developing an accurate combinatorial model of worm propagation that can facilitate the analysis of worm control strategies, (2) Building an accurate epidemiological model for the propagation of a worm employing local strategies, (3) Devising distributed architecture and algorithms for detection of worm scanning activities, (4) Designing effective control strategies against the worm, and (5) Simulation of the developed models and strategies on large, scale-free graphs representing real-world communication networks. The proposed pair-approximation model uses the information about the network structure--order, size, degree distribution, and transitivity. The empirical study of propagation on large scale-free graphs is in agreement with the theoretical analysis of the proposed pair-approximation model. We, then, describe a natural generalization of the classical cops-and-robbers game--a combinatorial model of worm propagation and control. With the help of this game on graphs, we show that the problem of containing the worm is NP-hard. Six novel near-optimal control strategies are devised: combination of static and dynamic immunization, reactive dynamic and invariant dynamic immunization, soft quarantining, predictive traffic-blocking, and contact-tracing. The analysis of the predictive dynamic traffic-blocking, employing only local information, shows that the worm can be contained so that 40\% of the network nodes are not affected. Finally, we develop the Detection via Distributed Blackholes architecture and algorithm which reflect the propagation strategy used by the worm and the salient properties of the network. Our distributed detection algorithm can detect the worm scanning activity when only 1.5% of the network has been affected by the propagation. The proposed models and algorithms are analyzed with an individual-based simulation of worm propagation on realistic scale-free topologies

The Offenders’ Perspective on Prevention: Guarding Against Victimization and Law Enforcement

Law-abiding citizens are concerned with deterring and preventing crime. One strategy to accomplish this goal is to increase the costs and reduce the benefits that particular situations present to offenders. This form of crime control is known as situational crime prevention. Like law-abiding persons, offenders must concern themselves with being victimized. Differently, however, offenders must also worry about being detected and punished by formal agents. Thus, situational prevention from the offenders’ perspective is relatively complex, encompassing efforts to block not only opportunities for victimization but also for law enforcement. Building on the work of Clarke, the present study uses qualitative data from drug dealers to illustrate how and why offenders use situational strategies and techniques to evade their adversaries. The article concludes by discussing implications for future work

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Breaking Up or Backing the Blue: A Content Analysis of Individual\u27s Views of the Police Abolition Movement

In the wake of the death of George Floyd, Breonna Taylor, and countless others there has been increased discussion regarding the scope and scale of policing in the United States. The defund the police movement has gained a substantial amount of traction in recent months as country wide protests and unrest has sparked the conversation of whether the police are fulfilling the sworn duties and more broadly what the public expect of the police. While individuals increasingly debate the merits of defunding and abolishing the police, what is less clear is whether people support the police abolition movement in the U.S. and the justifications for their views. An op-ed in the New York Times arguing that the U.S. should abolish the police provides an opportunity to better understand public opinion regarding this issue. A content analysis of almost 2,000 reader comments revealed that while some readers were supportive of the abolish movement in part due to the racist historical legacy of law enforcement, many others felt the proposal was radical and would have a series of negative consequences. In addition to those calling for reimaging how the police and to reconsider the types of incidents they handle; a common refrain from readers was the notion that crime would increase. Lastly, others worried the framing and focus on police abolition was unnecessarily divisive and would undermine what they consider more realistic reforms