Some remarks on cops and drunk robbers

The cops and robbers game has been extensively studied under the assumption of optimal play by both the cops and the robbers. In this paper we study the problem in which cops are chasing a drunk robber (that is, a robber who performs a random walk) on a graph. Our main goal is to characterize the "cost of drunkenness." Specifically, we study the ratio of expected capture times for the optimal version and the drunk robber one. We also examine the algorithmic side of the problem; that is, how to compute near-optimal search schedules for the cops. Finally, we present a preliminary investigation of the invisible robber game and point out differences between this game and graph search

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

A probabilistic version of the game of Zombies and Survivors on graphs

We consider a new probabilistic graph searching game played on graphs, inspired by the familiar game of Cops and Robbers. In Zombies and Survivors, a set of zombies attempts to eat a lone survivor loose on a given graph. The zombies randomly choose their initial location, and during the course of the game, move directly toward the survivor. At each round, they move to the neighbouring vertex that minimizes the distance to the survivor; if there is more than one such vertex, then they choose one uniformly at random. The survivor attempts to escape from the zombies by moving to a neighbouring vertex or staying on his current vertex. The zombies win if eventually one of them eats the survivor by landing on their vertex; otherwise, the survivor wins. The zombie number of a graph is the minimum number of zombies needed to play such that the probability that they win is strictly greater than 1/2. We present asymptotic results for the zombie numbers of several graph families, such as cycles, hypercubes, incidence graphs of projective planes, and Cartesian and toroidal grids

Statistical Model Checking for Cops and Robbers Game on Random Graph Models

Cops and robbers problem has been studied over the decades with many variants and applications in graph searching problem. In this work, we study a variant of cops and robbers problem on graphs. In this variant, there are di�erent types of cops and a minimum number of each type of cops are required to catch a robber. We studied this model over various random graph models and analyzed the properties using statistical model checking. To the best of our knowledge this variant of the cops and robber problem has not been studied yet. We have used statistical techniques to estimate the probability of robber getting caught in di�erent random graph models. We seek to compare the ease of catching robbers performing random walk on graphs, especially complex networks. In this work, we report the experiments that yields interesting empirical results. Through the experiments we have observed that it is easier to catch a robber in Barab�asi Albert model than in Erd�os-R�enyi graph model. We have also experimented with k-Regular graphs and real street networks. In our work, the model is framed as the multi-agent based system and we have implemented a statistical model checker, SMCA tool which veri�es agents based systems using statistical techniques. SMCA tool can take the model in JAVA programming language and support Probabilistic - Bounded LTL logic for property specification

An exploratory study into the commonalities of the life scripts of adolescent delinquents in selected institutions

Transactional analysis has been a useful tool for the researcher in categorizing these characteristics. Using it, he was able to recognize both commonalities and differences between types of problem adolescents. The purpose of this thesis is to examine the life scripts of problem adolescents of selected institutions to determine what the commonalities are within and between the categories of injunctions, counter injunctions, basic positions, rackets, games, decisions, programs of life course, and treatment contracts. The purpose and problem are embodied in four basic questions: (1) Do commonalities exist in the categories of injunctions, counter injunctions, basic positions, rackets, games, decision, programs of life course and treatment contracts?; (2) What are the most prevalent commonalities within each category? Example: What is the most common injunction?; (3) What are the commonalities between categories? Example: What is the most common game when the injunction is “Don’t get close?”; and (4) What are the commonalities among total life scripts? Calude Steiner categorizes the alcoholic into three main types: “drunk proud,” “lush,” and “wino;” is it possible to categorize adolescent delinquents into similar personality patterns

Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn

Present Tense : crime fiction in postapartheid South Africa

Since 1994, when South Africa transitioned from apartheid to majority rule, its locally written crime fiction has become a literary force. Although some critics initially dismissed the genre as superficialand clichéd, most now agree it offers important social, political and ethical insights, providing an arena in which shared issues may be theorised and thought through. These include, for example, the implications of the Truth and Reconciliation Commission, the loss of faith in governance and the rule of law, issues surrounding race and whiteness, and South Africa’s emergence out of isolation and into the larger world. Less well considered, however, is how crime fiction achieves those ends, and that is the focus of this thesis. It argues that the genre’s hermeneutic conventions, far from being reductive, are powerful tools for conveying social insight because these conventions, when adapted by writers or affected by context, change from text to text, and readers use these intertextual differences to interpret meaning. Together with the genre’s concentration on the collective, on morality, and on law and order, such engagement with the conventions helps readers decipher and in some cases find positive proposals for managing the country’s recovery narrative. After locating South African crime fiction historically and critically, I present my argument firstly through a close critical examination of novels by two South African crime writers, Andrew Brown and Mike Nicol, and then creatively, through my own crime novel, Present Tense. In contrast to Brown, who exaggerates features of the conventional police detective in order to highlight aspectsof identity and belonging in present day South Africa, Nicol subverts most of the conventions of the thriller to offer a searing and pessimistic critique of South African society. Present Tense, a police procedural, adapts conventions relating to the setting, protagonist and narrative resolution in order to address the present-day consequences of apartheid, notions of trust and betrayal, and the dislocation felt by white citizens in the new social order. Thus, paradoxically, the seemingly inflexible conventions of crime fiction enable nuanced comment on social issues at a particular place and time; and this ability ensures the genre’s relevance and importance to a post-traumatic, postcolonial society like South Africa. ACCESS TO THE NOVEL, PRESENT TENSE, IS RESTRICTED