In Chapter 1 it was shown that Fisk's proof of the art gallery theorem can be converted into an algorithm that covers a polygon of n vertices with [n/3\ guards in O{n logn) time. Although [n/3\ is necessary in some cases, often this is far more guards than are needed to cover a particular polygon. For example, convex polygons only require one guard, but Avis and Toussaint's algorithm would stil...

This paper presents a novel method for deciding the locations of “guards” required to visually inspect a given 2D workspace. The decided guard positions can then be used as control points in the path of a mobile robot that autonomously inspects a workspace. It is assumed that each of the guards (or the mobile robot that visits the guard positions in some order) is equipped with a panoramic came...

In the Eternal Domination game, a team of guard tokens initially occupies a dominating set on a graph G. A rioter then picks a node without a guard on it and attacks it. The guards defend against the attack: one of them has to move to the attacked node, while each remaining one can choose to move to one of his neighboring nodes. The new guards’ placement must again be dominating. This attack-de...

It has long been recognised that standard process algebra has difficulty dealing with actions of different priority, such as for instance an interrupt action of high priority. Various solutions have been proposed. We introduce a new approach, involving the addition of “priority guards” to Milner’s process calculus CCS. In our approach, priority is unstratified, meaning that actions are not assi...

Since Professor Lillemor Hallberg and Professor Karin Dahlberg started the International Journal of Qualitative Studies on Health and Well-being (IJQHW) in 2006 it has developed immensely, not least after 2010 when it became Open Access. With unhindered access to all content, readers in 172 countries have since then accessed the journal’s website in their thousands, and more than 290,000 full-t...

Given a graph and a single watchman, the objective of the Watchman’s Walk Problem is to find a closed dominating walk of minimum length which the watchman can traverse to efficiently guard the graph. When multiple guards are available, one natural variation is to assume fixed time constraints on the monitoring of vertices and attempt to minimize the number of guards required. We find upper boun...

In this discrete time process, guards are allowed to traverse edges of a network under the constraint that the neighbourhood of each vertex must be visited within a specified time interval t. Setting t = 0 the guards form a dominating set at all times. We show every rooted tree with relatively few leaves has a branch with a certain order and number of pendant vertices. This result is used to es...

There has been a growing interest in defining models of automata enriched with time. For instance, timed automata were introduced as automata extended with clocks. In this paper, we study models of timed finite state machines (TFSMs), i.e., FSMs enriched with time, which accept timed input words and generate timed output words. Here we discuss some models of TFSMs with a single clock: TFSMs wit...

We introduce the calculus of concurrent nets as an extension of the fusion calculus in which usual prefixing is replaced by arbitrary monotonic guards. Then we use this formalism to describe the prefixing policy of standard calculi as a particular form of communication. By developing a graphical syntax, we sharpen the geometric intuition and finally we provide an encoding of these guards as cau...

We introduce the calculus of concurrent nets as an extension of the fusion calculus in which usual prefixing is replaced by arbitrary monotonic guards. Then we use this formalism to describe the prefixing policy of standard calculi as a particular form of communication. By developing a graphical syntax, we sharpen the geometric intuition and finally we provide an encoding of these guards as cau...