Meeting in a Polygon by Anonymous Oblivious Robots

The Meeting problem for $k\geq 2$ searchers in a polygon $P$ (possibly with holes) consists in making the searchers move within $P$, according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions. The polygon is initially unknown to the searchers, and its edges obstruct both movement and vision. Depending on the shape of $P$, we minimize the number of searchers $k$ for which the Meeting problem is solvable. Specifically, if $P$ has a rotational symmetry of order $\sigma$ (where $\sigma=1$ corresponds to no rotational symmetry), we prove that $k=\sigma+1$ searchers are sufficient, and the bound is tight. Furthermore, we give an improved algorithm that optimally solves the Meeting problem with $k=2$ searchers in all polygons whose barycenter is not in a hole (which includes the polygons with no holes). Our algorithms can be implemented in a variety of standard models of mobile robots operating in Look-Compute-Move cycles. For instance, if the searchers have memory but are anonymous, asynchronous, and have no agreement on a coordinate system or a notion of clockwise direction, then our algorithms work even if the initial memory contents of the searchers are arbitrary and possibly misleading. Moreover, oblivious searchers can execute our algorithms as well, encoding information by carefully positioning themselves within the polygon. This code is computable with basic arithmetic operations, and each searcher can geometrically construct its own destination point at each cycle using only a compass. We stress that such memoryless searchers may be located anywhere in the polygon when the execution begins, and hence the information they initially encode is arbitrary. Our algorithms use a self-stabilizing map construction subroutine which is of independent interest.Comment: 37 pages, 9 figure

Distributed partitioning strategies in camera network application

In the first part we deal with the problem of patrolling a perimeter. We propose a distributed algorithm that assign to each camera a portion of the perimeter and converge to an equitable partition. Physical and covering constraints are kept into account. The protocol of comunication is asymmetric. In the first part we generalize this problem to a 2D discretized environment. Two distributed euristic are proposed to reach an equitable partition using symmetric and asymmetric communication. Effort are made in order to obtain areas with a regular and 'fat' shap

Multi-robot Patrol via the Metropolis-Hastings Algorithm

The problem of multi-robot patrol is a growing field of study that focuses on the problem of coordinating teams of robots to optimally patrol a perimeter or area. In this paper, we propose a new method of generating patrolling policies in the form of Markov chains via the Metropolis-Hastings algorithm. Our proposed method generates non-deterministic patrolling policies with the purpose of minimizing the probability of adversarial attack to a given area. We compare our method to a wide variety of approaches to patrolling methods on a large set of graphs in order to test the effectiveness of Markov chains as a patrolling policy

A Loss of the HMCS \u3cem\u3eClayoquot\u3c/em\u3e

The torpedo struck without warning. HMCS Clayoquot was returning from an anti-submarine sweep in the approaches to Halifax harbour when its stern rose into the air, mangled by the detonation of a German T-5 acoustic homing torpedo. The men aboard felt two concussions, the second likely being depth charges stored on Clayoquot’s stern set off by the torpedo. Whatever the details, the explosions were devastating for the small Bangor class minesweeper. A grainy photograph of the doomed ship shows the stern blasted vertical, the ship listing to starboard. Clayoquot lasted barely ten minutes after being hit, just long enough for all but eight of her crew to escape. The worst fate befell two young officers trapped in the port forward-cabin. These men called out through a port hole for axes to chop their way to freedom, but all the axes were underwater. The merciless sea closed around them as the ship vanished

The Fagnano Triangle Patrolling Problem

We investigate a combinatorial optimization problem that involves patrolling the edges of an acute triangle using a unit-speed agent. The goal is to minimize the maximum (1-gap) idle time of any edge, which is defined as the time gap between consecutive visits to that edge. This problem has roots in a centuries-old optimization problem posed by Fagnano in 1775, who sought to determine the inscribed triangle of an acute triangle with the minimum perimeter. It is well-known that the orthic triangle, giving rise to a periodic and cyclic trajectory obeying the laws of geometric optics, is the optimal solution to Fagnano's problem. Such trajectories are known as Fagnano orbits, or more generally as billiard trajectories. We demonstrate that the orthic triangle is also an optimal solution to the patrolling problem. Our main contributions pertain to new connections between billiard trajectories and optimal patrolling schedules in combinatorial optimization. In particular, as an artifact of our arguments, we introduce a novel 2-gap patrolling problem that seeks to minimize the visitation time of objects every three visits. We prove that there exist infinitely many well-structured billiard-type optimal trajectories for this problem, including the orthic trajectory, which has the special property of minimizing the visitation time gap between any two consecutively visited edges. Complementary to that, we also examine the cost of dynamic, sub-optimal trajectories to the 1-gap patrolling optimization problem. These trajectories result from a greedy algorithm and can be implemented by a computationally primitive mobile agent

The Breach of Security at San Jose’s Airport Raises Broader Issues

This Transportation Security Perspective is the fifth in a continuing series produced by the National Transportation Safety and Security Center of the Mineta Transportation Institute. These examine major terrorist attacks and trends in terrorists targeting surface transportation. Previous perspectives include the bus attack in Abuja, Nigeria, the terrorist bombings in Volgograd, Russia; the assault on passengers at the Kunming train station in China; and more