Variations on Cops and Robbers

We consider several variants of the classical Cops and Robbers game. We treat the version where the robber can move R > 1 edges at a time, establishing a general upper bound of N / \alpha ^{(1-o(1))\sqrt{log_\alpha N}}, where \alpha = 1 + 1/R, thus generalizing the best known upper bound for the classical case R = 1 due to Lu and Peng. We also show that in this case, the cop number of an N-vertex graph can be as large as N^{1 - 1/(R-2)} for finite R, but linear in N if R is infinite. For R = 1, we study the directed graph version of the problem, and show that the cop number of any strongly connected digraph on N vertices is at most O(N(log log N)^2/log N). Our approach is based on expansion.Comment: 18 page

Locating a robber with multiple probes

We consider a game in which a cop searches for a moving robber on a connected graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any $n$-vertex graph $G$ there is a winning strategy for the cop on the graph $G^{1/m}$ obtained by replacing each edge of $G$ by a path of length $m$, if $m\geq n$. The present authors showed that, for all but a few small values of $n$, this bound may be improved to $m\geq n/2$, which is best possible. In this paper we consider the natural extension in which the cop probes a set of $k$ vertices, rather than a single vertex, at each turn. We consider the relationship between the value of $k$ required to ensure victory on the original graph and the length of subdivisions required to ensure victory with $k=1$. We give an asymptotically best-possible linear bound in one direction, but show that in the other direction no subexponential bound holds. We also give a bound on the value of $k$ for which the cop has a winning strategy on any (possibly infinite) connected graph of maximum degree $\Delta$, which is best possible up to a factor of $(1-o(1))$.Comment: 16 pages, 2 figures. Updated to show that Theorem 2 also applies to infinite graphs. Accepted for publication in Discrete Mathematic

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

Spartan Daily, November 7, 1986

Volume 87, Issue 51https://scholarworks.sjsu.edu/spartandaily/7508/thumbnail.jp

The Harmful Side Effects of Drug Prohibition

Some drugs make people feel good. That is why some people use them. Some of these drugs are alleged to have side effects so destructive that many advise against their use. The same may be said about statutes that attempt to prohibit the manufacture, sale, and use of drugs. Advocating drug prohibition makes some people feel good because they think they are “doing something” about what they believe to be a serious social problem. Others who support these laws are not so altruistically motivated. Employees of law enforcement bureaus and academics who receive government grants to study drug use, for example, may gain financially from drug prohibition. But as with using drugs, using drug laws can have moral and practical side effects so destructive that they argue against ever using legal institutions in this manner. This Article will not attempt to identify and “weigh” the costs of drug use against the costs of drug laws. Instead, it will focus exclusively on identifying the harmful side effects of drug law enforcement and showing why these effects are unavoidable. So one-sided a treatment is justified for two reasons. First, a cost-benefit or cost-cost analysis may simply be impossible. Second, discussions by persons who support illegalizing drugs usually emphasize only the harmful effects of drug use while largely ignoring the serious costs of such policies. By exclusively relating the other side of the story, this Article is intended to inject some balance into the normal debate. The harmful side-effects of drug laws have long been noted by a number of commentators, although among the general public the facts are not as well known as they should be. More importantly, even people who agree about the facts fail to grasp that it is the nature of the means—coercion—chosen to pursue the suppression of voluntary consumptive activity that makes these effects unavoidable. This vital and overlooked connection is the main subject of this Article

Global ethics and global strangers : beyond the inter-national relations framework : an essay in descriptive ethics

ethics;globalization;boundaries;individuals;international relations

Application of Routine Activities Theory to the Study of Residential Armed Robbery in Ghana

This study utilized Routine Activities theory to explain deterrent and motivating factors associated with residential armed robbery in Ghana. Although several studies have examined crime through the lenses of Routine Activities theory, none such studies have been dedicated to the study of residential armed robbery in Ghana. This study, therefore, attempts to fill that void by applying Routine Activities theory to the study of residential armed robbery. This research samples 56 of armed robbers in three selected prisons of contemporary Ghana to provide a fuller criminological and descriptive analysis of the offence, the offenders, motivation and guardianship to committing residential armed robbery. Findings indicate substantial evidence that motivated offenders were deterred from violating hardened targets with the presence of capable guardianship. Limitations and suggestions for further research are discussed as well

The Becker Paradox and Type I vs. Type II Errors in the Economics of Crime

Two real-world observations are not easily replicated in models of crime. First, although capital punishment is optimal in Becker’s (1968) model, it is rarely observed in the real world. Second, criminal procedure and the evaluation of evidence vary across societies and historical periods, the standard of proof being sometimes very high and sometimes quite low. In this paper, we develop a general equilibrium model of judicial procedure allowing for innocent persons being convicted. We show that the median voter theorem applies to this model, making judicial procedure endogenous. So formulated, the model can replicate both empirical observations.Criminal law; Judicial error; Burden of proof