Evacuation of Equilateral Triangles by Mobile Agents of Limited Communication Range

We consider the problem of evacuating $k \geq 2$ mobile agents from a unit-sided equilateral triangle through an exit located at an unknown location on the perimeter of the triangle. The agents are initially located at the centroid of the triangle. An agent can move at speed at most one, and finds the exit only when it reaches the point where the exit is located. The agents can collaborate in the search for the exit. The goal of the {\em evacuation problem} is to minimize the evacuation time, defined as the worst-case time for {\em all} the agents to reach the exit. Two models of communication between agents have been studied before; {\em non-wireless} or {\em face-to-face communication} model and {\em wireless communication} model. In the former model, agents can exchange information about the location of the exit only if they are at the same point at the same time, whereas in the latter model, the agents can send and receive information about the exit at any time regardless of their positions in the domain. In this thesis, we propose a new and more realistic communication model: agents can communicate with other agents at distance at most $r$ with $0\leq r \leq 1$. We propose and analyze several algorithms for the problem of evacuation by $k \geq 2$ agents in this model; our results indicate that the best strategy to be used varies depending on the values of $r$ and $k$. For two agents, we give five strategies, the last of which achieves the best performance among all the five strategies for all sub-ranges of $r$ in the range $0 < r \leq 1$. We also show a lower bound on the evacuation time of two agents for any $r 2$ agents, we study three strategies for evacuation: in the first strategy, called {\sf X3C}, agents explore all three sides of the triangle before connecting to exchange information; in the second strategy, called {\sf X1C}, agents explore a single side of the triangle before connecting; in the third strategy, called {\sf CXP}, the agents travel to the perimeter to locations in which they are connected, and explore it while always staying connected. For 3 or 4 agents, we show that X3C works better than X1C for small values of $r$, while X1C works better for larger values of $r$. Finally, we show that for any $r$, evacuation of $k=6 +2\lceil(\frac{1}{r}-1)\rceil$ agents can be done using the CXP strategy in time $1+\sqrt{3}/3$, which is optimal in terms of time, and asymptotically optimal in terms of the number of agents

Triangle Evacuation of 2 Agents in the Wireless Model

The input to the \emph{Triangle Evacuation} problem is a triangle $ABC$. Given a starting point $S$ on the perimeter of the triangle, a feasible solution to the problem consists of two unit-speed trajectories of mobile agents that eventually visit every point on the perimeter of $ABC$. The cost of a feasible solution (evacuation cost) is defined as the supremum over all points $T$ of the time it takes that $T$ is visited for the first time by an agent plus the distance of $T$ to the other agent at that time. Similar evacuation type problems are well studied in the literature covering the unit circle, the $\ell_p$ unit circle for $p\geq 1$, the square, and the equilateral triangle. We extend this line of research to arbitrary non-obtuse triangles. Motivated by the lack of symmetry of our search domain, we introduce 4 different algorithmic problems arising by letting the starting edge and/or the starting point $S$ on that edge to be chosen either by the algorithm or the adversary. To that end, we provide a tight analysis for the algorithm that has been proved to be optimal for the previously studied search domains, as well as we provide lower bounds for each of the problems. Both our upper and lower bounds match and extend naturally the previously known results that were established only for equilateral triangles

Group Evacuation on a Line by Agents with Different Communication Abilities

We consider evacuation of a group of n ? 2 autonomous mobile agents (or robots) from an unknown exit on an infinite line. The agents are initially placed at the origin of the line and can move with any speed up to the maximum speed 1 in any direction they wish and they all can communicate when they are co-located. However, the agents have different wireless communication abilities: while some are fully wireless and can send and receive messages at any distance, a subset of the agents are senders, they can only transmit messages wirelessly, and the rest are receivers, they can only receive messages wirelessly. The agents start at the same time and their communication abilities are known to each other from the start. Starting at the origin of the line, the goal of the agents is to collectively find a target/exit at an unknown location on the line while minimizing the evacuation time, defined as the time when the last agent reaches the target. We investigate the impact of such a mixed communication model on evacuation time on an infinite line for a group of cooperating agents. In particular, we provide evacuation algorithms and analyze the resulting competitive ratio (CR) of the evacuation time for such a group of agents. If the group has two agents of two different types, we give an optimal evacuation algorithm with competitive ratio CR = 3+2?2. If there is a single sender or fully wireless agent, and multiple receivers we prove that CR ? [2+?5,5], and if there are multiple senders and a single receiver or fully wireless agent, we show that CR ? [3,5.681319]. Any group consisting of only senders or only receivers requires competitive ratio 9, and any other combination of agents has competitive ratio 3

God Save the Queen

Queen Daniela of Sardinia is asleep at the center of a round room at the top of the tower in her castle. She is accompanied by her faithful servant, Eva. Suddenly, they are awakened by cries of "Fire". The room is pitch black and they are disoriented. There is exactly one exit from the room somewhere along its boundary. They must find it as quickly as possible in order to save the life of the queen. It is known that with two people searching while moving at maximum speed 1 anywhere in the room, the room can be evacuated (i.e., with both people exiting) in 1 + (2 pi)/3 + sqrt{3} ~~ 4.8264 time units and this is optimal [Czyzowicz et al., DISC\u2714], assuming that the first person to find the exit can directly guide the other person to the exit using her voice. Somewhat surprisingly, in this paper we show that if the goal is to save the queen (possibly leaving Eva behind to die in the fire) there is a slightly better strategy. We prove that this "priority" version of evacuation can be solved in time at most 4.81854. Furthermore, we show that any strategy for saving the queen requires time at least 3 + pi/6 + sqrt{3}/2 ~~ 4.3896 in the worst case. If one or both of the queen\u27s other servants (Biddy and/or Lili) are with her, we show that the time bounds can be improved to 3.8327 for two servants, and 3.3738 for three servants. Finally we show lower bounds for these cases of 3.6307 (two servants) and 3.2017 (three servants). The case of n >= 4 is the subject of an independent study by Queen Daniela\u27s Royal Scientific Team

Distributed Systems and Mobile Computing

The book is about Distributed Systems and Mobile Computing. This is a branch of Computer Science devoted to the study of systems whose components are in different physical locations and have limited communication capabilities. Such components may be static, often organized in a network, or may be able to move in a discrete or continuous environment. The theoretical study of such systems has applications ranging from swarms of mobile robots (e.g., drones) to sensor networks, autonomous intelligent vehicles, the Internet of Things, and crawlers on the Web. The book includes five articles. Two of them are about networks: the first one studies the formation of networks by agents that interact randomly and have the ability to form connections; the second one is a study of clustering models and algorithms. The three remaining articles are concerned with autonomous mobile robots operating in continuous space. One article studies the classical gathering problem, where all robots have to reach a common location, and proposes a fast algorithm for robots that are endowed with a compass but have limited visibility. The last two articles deal with the evacuations problem, where two robots have to locate an exit point and evacuate a region in the shortest possible time

Practical Considerations and Applications for Autonomous Robot Swarms

In recent years, the study of autonomous entities such as unmanned vehicles has begun to revolutionize both military and civilian devices. One important research focus of autonomous entities has been coordination problems for autonomous robot swarms. Traditionally, robot models are used for algorithms that account for the minimum specifications needed to operate the swarm. However, these theoretical models also gloss over important practical details. Some of these details, such as time, have been considered before (as epochs of execution). In this dissertation, we examine these details in the context of several problems and introduce new performance measures to capture practical details. Specifically, we introduce three new metrics: (1) the distance complexity (reflecting power usage and wear-and-tear of robots), (2) the spatial complexity (reflecting the space needed for the algorithm to work), and (3) local computational complexity (reflecting the computational requirements for each robot in the swarm). We apply these metrics in the study of some well-known and important problems, such as Complete Visibility and Arbitrary Pattern Formation. We also introduce and study a new problem, Doorway Egress, that captures the essence of a swarm’s navigation through restricted spaces. First, we examine the distance and spatial complexity used across a class of Complete Visibility algorithms. Second, we provide algorithms for Complete Visibility on an integer plane, including some that are asymptotically optimal in terms of time, distance complexity, and spatial complexity. Third, we introduce the problem of Doorway Egress and provide algorithms for a variety of robot swarm models with various optimalities. Finally, we provide an optimal algorithm for Arbitrary Pattern Formation on the grid

Mobility Problems in Distributed Search and Combinatorial Games

This thesis examines a collection of topics under the general notion of mobility of agents. We examine problems where a set of entities, perceived as robots or tokens, navigate in some given (discrete or continuous) environment to accomplish a goal. The problems we consider fall under two main research fields. First, Distributed Search where the agents cooperate to explore their environment or search for a specific target location within it. Second, Combinatorial Games, in the spirit of Pursuit-Evasion, where the agents are now divided into two groups with complementary objectives competing against each other. More specifically, we consider three distinct problems: disk evacuation, exploration of dynamic graphs and eternal domination. In Disk Evacuation, two robots with different speeds aim to discover an unknown exit lying on the boundary of a unit disk. For a wide range of speeds, we provide matching upper and lower bounds. In Dynamic Graph Exploration, we analyze the exploration time for a randomly-walking agent wishing to visit all the vertices of a stochastically-evolving graph. In Eternal Domination, we consider rectangular grid graphs and upper bound the amount of guard agents needed to perpetually defend the vertices against an attacker

Poster abstract research showcase College of Science and Technology

Welcome to the College of Science and Technology Research and Innovation Showcase 2014, an event which celebrates the research achievements of our science disciplines. Our research brings together scientists from architecture and the built environment through to computing, engineering, mathematics and physics and biology, geography and environmental science. We are committed to build on our strengths, and our key vision is to drive research growth and impact through exploitation of the synergy between research, innovation and enterprise. This year’s showcase event includes over 70 posters illustrating the excellent research being pursued, a Dean's prize recognising the achievements of an early career researcher, prizes for the best student and best students’ posters and journal papers, and this proceedings of abstracts showing the high quality and range of research in the College of Science and Technology