We consider variants of the art gallery problem where guard visibility is limited to a certain angular aperture α. We show that the problem is NP-hard even when guards can be located in the interior of the polygon. We then proceed to prove that both this problem and its vertex variant, where guard placement is restricted to the vertices of the polygon, are APX-hard. We observe that earlier cons...

We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be red only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form yi #yj + ci;j where yi is either x 0 i or xi, the values of the counter i respectively after and before the transition, and # is any relational symbo...

Pattern mat hing is a well-appre iated feature of languages like ML or Haskell; it greatly simpli es the task of inspe ting values of stru tured data types and fa ilitates su in t fun tion de nitions that are easy to understand. In its basi form, pattern mat hing tries to identify a ertain stru ture of a value to be pro essed by a fun tion. This stru ture is spe i ed by a pattern, and if it an ...

Protection of software code against illegitimate modifications by its users is a pressing issue to many software developers. Many software-based mechanisms for protecting program code are too weak (e.g., they have single points of failure) or too expensive to apply (e.g., they incur heavy runtime performance penalty to the protected programs). In this paper, we present and explore a methodology...

Consider an art gallery formed by a polygon on n vertices with m pairs of vertices joined by interior diagonals, the interior walls. Each interior wall has an arbitrarily placed, arbitrarily small doorway. We will show that the minimum number of guards that suffice to guard all art galleries with n vertices and m interior walls is min{b(2n−3)/3c, b(2n+m−2)/4c, b(2m+n)/3c}. If we restrict oursel...

BACKGROUND Several studies have examined the prevalence and pattern of substance use among medical students in Nigeria. Few of these studies have specifically examined the relationship between the psychological distress and psychoactive substance use among these students. Yet, evidence world-wide suggests that substance use among medical students might be on the rise and may be related to the l...

“Entry” guards protect the Tor onion routing system from variants of the “predecessor” attack, that would allow an adversary with control of a fraction of routers to eventually de-anonymize some users. Research has however shown the three guard scheme has drawbacks and Dingledine et al. proposed in 2014 for each user to have a single long-term guard. We first show that such a guard selection st...

In this paper we consider the problem of monitoring an art gallery modeled as a polygon, the edges of which are arcs of curves, with edge or mobile guards. Our focus is on piecewise-convex polygons, i.e., polygons that are locally convex, except possibly at the vertices, and their edges are convex arcs. We transform the problem of monitoring a piecewise-convex polygon to the problem of 2dominat...

The popularity of snowboarding has brought awareness to injuries sustained during the sport. Wrist injuries are among the most common injuries, and there is an interest in using protective equipment to prevent these injuries. The purpose of this study was to review the literature on wrist guard use, injury prevention, the biomechanical effects of wrist guards, and the various types of wrist gua...