E. Kranakis

J. Czyzowicz, R. Killick, E. Kranakis et al.

There are $n\geq 3$ unit speed mobile agents placed at the origin of the infinite line. In as little time as possible, the agents must find and evacuate from an exit placed at an initially unknown location on the line. The agents can communicate in the wireless mode in order to facilitate the evacuation (i.e. by announcing the target's location when it is found). However, among the agents are a subset of at most $f$ crash faulty agents who may fail to announce the target when they visit its location. In this paper we study this aforementioned problem for the specific case that $n=2f+1$. We introduce a novel type of search algorithm and analyze its competitive ratio -- the supremum, over all possible target locations, of the ratio of the time the agents take to evacuate divided by the initial distance between the agents and the target. In particular, we demonstrate that the competitive ratio of evacuation is at most $7.437011$ for $(n,f)=(3,1)$; at most $7.253767$ for $(n,f)=(5,2)$ and $(7,3)$; and at most $7.147026$ for $(n,f)=(9,4)$. For larger values of $n=2f+1$ we prove an asymptotic upper bound of $4+2\sqrt{2}$. We also adapt our evacuation algorithm for $(n,f)=(3,1)$ to the problem of search by three agents with one byzantine fault, i.e. the faulty agent may also lie about finding the target. In doing so we improve the best known upper bound on this search problem from 8.653055 to 7.437011.

J. Czyzowicz, K. Georgiou, R. Killick et al.

We introduce and study a new search-type problem with ($n+1$)-robots on a disk. The searchers (robots) all start from the center of the disk, have unit speed, and can communicate wirelessly. The goal is for a distinguished robot (the queen) to reach and evacuate from an exit that is hidden on the perimeter of the disk in as little time as possible. The remaining $n$ robots (servants) are there to facilitate the queen's objective and are not required to reach the hidden exit. We provide upper and lower bounds for the time required to evacuate the queen from a unit disk. Namely, we propose an algorithm specifying the trajectories of the robots which guarantees evacuation of the queen in time always better than $2 + 4(\sqrt{2}-1) \fracπ{n}$ for $n \geq 4$ servants. We also demonstrate that for $n \geq 4$ servants the queen cannot be evacuated in time less than $2+\fracπ{n}+\frac{2}{n^2}$.

J. Czyzowicz, E. Kranakis, D. Krizanc et al.

Cooperation between mobile robots and wireless sensor networks is a line of research that is currently attracting a lot of attention. In this context, we study the following problem of barrier coverage by stationary wireless sensors that are assisted by a mobile robot with the capacity to move sensors. Assume that $n$ sensors are initially arbitrarily distributed on a line segment barrier. Each sensor is said to cover the portion of the barrier that intersects with its sensing area. Owing to incorrect initial position, or the death of some of the sensors, the barrier is not completely covered by the sensors. We employ a mobile robot to move the sensors to final positions on the barrier such that barrier coverage is guaranteed. We seek algorithms that minimize the length of the robot's trajectory, since this allows the restoration of barrier coverage as soon as possible. We give an optimal linear-time offline algorithm that gives a minimum-length trajectory for a robot that starts at one end of the barrier and achieves the restoration of barrier coverage. We also study two different online models: one in which the online robot does not know the length of the barrier in advance, and the other in which the online robot knows the length of the barrier. For the case when the online robot does not know the length of the barrier, we prove a tight bound of $3/2$ on the competitive ratio, and we give a tight lower bound of $5/4$ on the competitive ratio in the other case. Thus for each case we give an optimal online algorithm.